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Inflation (cosmology)

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch is believed to have lasted from seconds to between  and  seconds  after the Big Bang. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago).

Inflation theory was developed in the late 1970s and early 80s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Alexei Starobinsky, Alan Guth, and Andrei Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation". It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation). Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed.

The detailed particle physics mechanism responsible for inflation is unknown. The basic inflationary paradigm is accepted by most physicists, as a number of inflation model predictions have been confirmed by observation; however, a substantial minority of scientists dissent from this position. The hypothetical field thought to be responsible for inflation is called the inflaton.

In 2002 three of the original architects of the theory were recognized for their major contributions; physicists Alan Guth of M.I.T., Andrei Linde of Stanford, and Paul Steinhardt of Princeton shared the Dirac Prize "for development of the concept of inflation in cosmology". In 2012 Guth and Linde were awarded the Breakthrough Prize in Fundamental Physics for their invention and development of inflationary cosmology.

Overview
Around 1930, Edwin Hubble discovered that light from remote galaxies was redshifted; the more remote, the more shifted. This implies that the galaxies are receding from the Earth, with more distant galaxies receding more rapidly, such that galaxies also recede from each other. This expansion of the universe was previously predicted by Alexander Friedmann and Georges Lemaître from the theory of general relativity. It can be understood as a consequence of an initial impulse, which sent the contents of the universe flying apart at such a rate that their mutual gravitational attraction has not reversed their separation.

Inflation may provide this initial impulse. According to the Friedmann equations that describe the dynamics of an expanding universe, a fluid with sufficiently negative pressure exerts gravitational repulsion in the cosmological context. A field in a positive-energy false vacuum state could represent such a fluid, and the resulting repulsion would set the universe into exponential expansion. This inflation phase was originally proposed by Alan Guth in 1979 because the exponential expansion could dilute exotic relics, such as magnetic monopoles, that were predicted by grand unified theories at the time. This would explain why such relics were not seen. It was quickly realized that such accelerated expansion would resolve the horizon problem and the flatness problem. These problems arise from the notion that to look like it does today, the Universe must have started from very finely tuned, or "special", initial conditions at the Big Bang.

Theory
An expanding universe generally has a cosmological horizon, which, by analogy with the more familiar horizon caused by the curvature of Earth's surface, marks the boundary of the part of the Universe that an observer can see. Light (or other radiation) emitted by objects beyond the cosmological horizon in an accelerating universe never reaches the observer, because the space in between the observer and the object is expanding too rapidly.

The observable universe is one causal patch of a much larger unobservable universe; other parts of the Universe cannot communicate with Earth yet. These parts of the Universe are outside our current cosmological horizon. In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view. Yet as a local observer sees such a region for the first time, it looks no different from any other region of space the local observer has already seen: its background radiation is at nearly the same temperature as the background radiation of other regions, and its space-time curvature is evolving lock-step with the others. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They could not have learned it by getting signals, because they were not previously in communication with our past light cone.

Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the cosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communication. The spatial slices are expanding very fast to cover huge volumes. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous.

As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero and space begins to expand normally. The new regions that come into view during the normal expansion phase are exactly the same regions that were pushed out of the horizon during inflation, and so they are at nearly the same temperature and curvature, because they come from the same originally small patch of space.

The theory of inflation thus explains why the temperatures and curvatures of different regions are so nearly equal. It also predicts that the total curvature of a space-slice at constant global time is zero. This prediction implies that the total ordinary matter, dark matter and residual vacuum energy in the Universe have to add up to the critical density, and the evidence supports this. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and many of these quantitative predictions have been confirmed.

Space expands
In a space that expands exponentially (or nearly exponentially) with time, any pair of free-floating objects that are initially at rest will move apart from each other at an accelerating rate, at least as long as they are not bound together by any force. From the point of view of one such object, the spacetime is something like an inside-out Schwarzschild black hole—each object is surrounded by a spherical event horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially).

In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the following metric:

ds^2=- (1- \Lambda r^2) \, c^2dt^2 + {1\over 1-\Lambda r^2} \, dr^2 + r^2 \, d\Omega^2. $$

This exponentially expanding spacetime is called a de Sitter space, and to sustain it there must be a cosmological constant, a vacuum energy density that is constant in space and time and proportional to Λ in the above metric. For the case of exactly exponential expansion, the vacuum energy has a negative pressure p equal in magnitude to its energy density ρ; the equation of state is p=−ρ.

Inflation is typically not an exactly exponential expansion, but rather quasi- or near-exponential. In such a universe the horizon will slowly grow with time as the vacuum energy density gradually decreases.

Few inhomogeneities remain
Because the accelerating expansion of space stretches out any initial variations in density or temperature to very large length scales, an essential feature of inflation is that it smooths out inhomogeneities and anisotropies, and reduces the curvature of space. This pushes the Universe into a very simple state in which it is completely dominated by the inflaton field and the only significant inhomogeneities are tiny quantum fluctuations. Inflation also dilutes exotic heavy particles, such as the magnetic monopoles predicted by many extensions to the Standard Model of particle physics. If the Universe was only hot enough to form such particles before a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the observable universe. Together, these effects are called the inflationary "no-hair theorem" by analogy with the no hair theorem for black holes.

The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon, except for not testable disagreements about what is on the other side. The interpretation of the no-hair theorem is that the Universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe, energy densities generally fall, or get diluted, as the volume of the Universe increases. For example, the density of ordinary "cold" matter (dust) goes down as the inverse of the volume: when linear dimensions double, the energy density goes down by a factor of eight; the radiation energy density goes down even more rapidly as the Universe expands since the wavelength of each photon is stretched (redshifted), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen (see the solution of the energy density continuity equation for an ultra-relativistic fluid). During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in everything else, including inhomogeneities, curvature, anisotropies, exotic particles, and standard-model particles is falling, and through sufficient inflation these all become negligible. This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.

Duration
A key requirement is that inflation must continue long enough to produce the present observable universe from a single, small inflationary Hubble volume. This is necessary to ensure that the Universe appears flat, homogeneous and isotropic at the largest observable scales. This requirement is generally thought to be satisfied if the Universe expanded by a factor of at least during inflation.

Reheating
Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model-dependent, but in the first models it was typically from K down to  K. ) This relatively low temperature is maintained during the inflationary phase. When inflation ends the temperature returns to the pre-inflationary temperature; this is called reheating or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles, including electromagnetic radiation, starting the radiation dominated phase of the Universe. Because the nature of the inflaton field is not known, this process is still poorly understood, although it is believed to take place through a parametric resonance.

Motivations
Inflation tries to resolve several problems in Big Bang cosmology that were discovered in the 1970s. Inflation was first proposed by Alan Guth in 1979 while investigating the problem of why no magnetic monopoles are seen today; he found that a positive-energy false vacuum would, according to general relativity, generate an exponential expansion of space. It was very quickly realised that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does today, the Universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the Universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.

Horizon problem
The horizon problem is the problem of determining why the universe appears statistically homogeneous and isotropic in accordance with the cosmological principle. For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. The situation is quite different in the big bang model without inflation, because gravitational expansion does not give the early universe enough time to equilibrate. In a big bang with only the matter and radiation known in the Standard Model, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than the speed of light and thus have never come into causal contact. In the early Universe, it was not possible to send a light signal between the two regions. Because they have had no interaction, it is difficult to explain why they have the same temperature (are thermally equilibrated). Historically, proposed solutions included the Phoenix universe of Georges Lemaître, the related oscillatory universe of Richard Chase Tolman, and the Mixmaster universe of Charles Misner. Lemaître and Tolman proposed that a universe undergoing a number of cycles of contraction and expansion could come into thermal equilibrium. Their models failed, however, because of the buildup of entropy over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universe more chaotic, could lead to statistical homogeneity and isotropy.

Flatness problem
The flatness problem is sometimes called one of the Dicke coincidences (along with the cosmological constant problem). It became known in the 1960s that the density of matter in the Universe was comparable to the critical density necessary for a flat universe (that is, a universe whose large scale geometry is the usual Euclidean geometry, rather than a non-Euclidean hyperbolic or spherical geometry).

Therefore, regardless of the shape of the universe the contribution of spatial curvature to the expansion of the Universe could not be much greater than the contribution of matter. But as the Universe expands, the curvature redshifts away more slowly than matter and radiation. Extrapolated into the past, this presents a fine-tuning problem because the contribution of curvature to the Universe must be exponentially small (sixteen orders of magnitude less than the density of radiation at Big Bang nucleosynthesis, for example). This problem is exacerbated by recent observations of the cosmic microwave background that have demonstrated that the Universe is flat to within a few percent.

Magnetic-monopole problem
The magnetic monopole problem, sometimes called "the exotic-relics problem", says that if the early universe were very hot, a large number of very heavy, stable magnetic monopoles would have been produced.

Stable magnetic monopoles are a problem for Grand Unified Theories, which propose that at high temperatures (such as in the early universe) the electromagnetic force, strong, and weak nuclear forces are not actually fundamental forces but arise due to spontaneous symmetry breaking from a single gauge theory. These theories predict a number of heavy, stable particles that have not been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "charge" of magnetic field.

Monopoles are predicted to be copiously produced following Grand Unified Theories at high temperature, and they should have persisted to the present day, to such an extent that they would become the primary constituent of the Universe. Not only is that not the case, but all searches for them have failed, placing stringent limits on the density of relic magnetic monopoles in the Universe.

A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: Monopoles would be separated from each other as the Universe around them expands, potentially lowering their observed density by many orders of magnitude. Though, as cosmologist Martin Rees has written,
 * "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!"

Precursors
In the early days of General Relativity, Albert Einstein introduced the cosmological constant to allow a static solution, which was a three-dimensional sphere with a uniform density of matter. Later, Willem de Sitter found a highly symmetric inflating universe, which described a universe with a cosmological constant that is otherwise empty. It was discovered that Einstein's universe is unstable, and that small fluctuations cause it to collapse or turn into a de Sitter universe.

In 1965, Erast Gliner proposed a unique assumption regarding the early Universe's pressure in the context of the Einstein-Friedmann equations. According to his idea, the pressure was negatively proportional to the energy density. This relationship between pressure and energy density served as the initial theoretical prediction of dark energy.

In the early 1970s, Zeldovich noticed the flatness and horizon problems of Big Bang cosmology; before his work, cosmology was presumed to be symmetrical on purely philosophical grounds. In the Soviet Union, this and other considerations led Belinski and Khalatnikov to analyze the chaotic BKL singularity in General Relativity. Misner's Mixmaster universe attempted to use this chaotic behavior to solve the cosmological problems, with limited success.

False vacuum
In the late 1970s, Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field theory. Like a metastable phase in statistical mechanics—water below the freezing temperature or above the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition. Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume. He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology.

The universe could have been spontaneously created from nothing (no space, time, nor matter) by quantum fluctuations of metastable false vacuum causing an expanding bubble of true vacuum.

Starobinsky inflation
In the Soviet Union, Alexei Starobinsky noted that quantum corrections to general relativity should be important for the early universe. These generically lead to curvature-squared corrections to the Einstein–Hilbert action and a form of f(R) modified gravity. The solution to Einstein's equations in the presence of curvature squared terms, when the curvatures are large, leads to an effective cosmological constant. Therefore, he proposed that the early universe went through an inflationary de Sitter era. This resolved the cosmology problems and led to specific predictions for the corrections to the microwave background radiation, corrections that were then calculated in detail. Starobinsky used the action

S=\frac{1}{2} \int d^4 x \left(R + \frac{R^2}{6M^2} \right) $$ which corresponds to the potential
 * $$\quad V(\phi)=\Lambda^4 \left(1 - e^{-\sqrt{2/3} \phi/M^2_p} \right)^2 $$

in the Einstein frame. This results in the observables: $$ n_s=1 - \frac{2}{N}, \quad \quad r=\frac{12}{N^2}.$$

Monopole problem
In 1978, Zeldovich noted the magnetic monopole problem, which was an unambiguous quantitative version of the horizon problem, this time in a subfield of particle physics, which led to several speculative attempts to resolve it. In 1980 Alan Guth realized that false vacuum decay in the early universe would solve the problem, leading him to propose a scalar-driven inflation. Starobinsky's and Guth's scenarios both predicted an initial de Sitter phase, differing only in mechanistic details.

Early inflationary models
Guth proposed inflation in January 1981 to explain the nonexistence of magnetic monopoles; it was Guth who coined the term "inflation". At the same time, Starobinsky argued that quantum corrections to gravity would replace the supposed initial singularity of the Universe with an exponentially expanding de Sitter phase. In October 1980, Demosthenes Kazanas suggested that exponential expansion could eliminate the particle horizon and perhaps solve the horizon problem, while Katsuhiko Sato suggested that an exponential expansion could eliminate domain walls (another kind of exotic relic). In 1981 Einhorn and Sato published a model similar to Guth's and showed that it would resolve the puzzle of the magnetic monopole abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions.

Guth proposed that as the early universe cooled, it was trapped in a false vacuum with a high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in a metastable state (it was supercooled), which it could only decay out of through the process of bubble nucleation via quantum tunneling. Bubbles of true vacuum spontaneously form in the sea of false vacuum and rapidly begin expanding at the speed of light. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate any radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch it is likely that only one bubble would nucleate.

"... Kazanas (1980) called this phase of the early Universe 'de Sitter's phase.' The name 'inflation' was given by Guth (1981). ... Guth himself did not refer to work of Kazanas until he published a book on the subject under the title The Inflationary Universe: The quest for a new theory of cosmic origin (1997), where he apologizes for not having referenced the work of Kazanas and of others, related to inflation."

Slow-roll inflation
The bubble collision problem was solved by Linde and independently by Andreas Albrecht and Paul Steinhardt in a model named new inflation or slow-roll inflation (Guth's model then became known as old inflation). In this model, instead of tunneling out of a false vacuum state, inflation occurred by a scalar field rolling down a potential energy hill. When the field rolls very slowly compared to the expansion of the Universe, inflation occurs. However, when the hill becomes steeper, inflation ends and reheating can occur.

Effects of asymmetries
Eventually, it was shown that new inflation does not produce a perfectly symmetric universe, but that quantum fluctuations in the inflaton are created. These fluctuations form the primordial seeds for all structure created in the later universe. These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov in analyzing Starobinsky's similar model. In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at Cambridge University. The fluctuations were calculated by four groups working separately over the course of the workshop: Stephen Hawking; Starobinsky; Guth and So-Young Pi; and Bardeen, Steinhardt and Turner.

Observational status
Inflation is a mechanism for realizing the cosmological principle, which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the cosmic microwave background made by the Planck spacecraft. This analysis shows that the Universe is flat to within $e$ percent, and that it is homogeneous and isotropic to one part in 100,000.

Inflation predicts that the structures visible in the Universe today formed through the gravitational collapse of perturbations that were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations, called a nearly-scale-invariant Gaussian random field is very specific and has only two free parameters. One is the amplitude of the spectrum and the spectral index, which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized de Sitter universe). The other free parameter is the tensor to scalar ratio. The simplest inflation models, those without fine-tuning, predict a tensor to scalar ratio near 0.1.

Inflation predicts that the observed perturbations should be in thermal equilibrium with each other (these are called adiabatic or isentropic perturbations). This structure for the perturbations has been confirmed by the Planck spacecraft, WMAP spacecraft and other cosmic microwave background (CMB) experiments, and galaxy surveys, especially the ongoing Sloan Digital Sky Survey. These experiments have shown that the one part in 100,000 inhomogeneities observed have exactly the form predicted by theory. There is evidence for a slight deviation from scale invariance. The spectral index, $e$$60$ is one for a scale-invariant Harrison–Zel'dovich spectrum. The simplest inflation models predict that $Einflation⁄T0$$T$ is between 0.92 and 0.98. This is the range that is possible without fine-tuning of the parameters related to energy. From Planck data it can be inferred that $0$$1⁄2$=0.968 ± 0.006, and a tensor to scalar ratio that is less than 0.11. These are considered an important confirmation of the theory of inflation.

Various inflation theories have been proposed that make radically different predictions, but they generally have much more fine-tuning than should be necessary. As a physical model, however, inflation is most valuable in that it robustly predicts the initial conditions of the Universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics.

Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year WMAP data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature. However, the third-year data revealed that the effect was a statistical anomaly. Another effect remarked upon since the first cosmic microwave background satellite, the Cosmic Background Explorer is that the amplitude of the quadrupole moment of the CMB is unexpectedly low and the other low multipoles appear to be preferentially aligned with the ecliptic plane. Some have claimed that this is a signature of non-Gaussianity and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to other new physics, foreground contamination, or even publication bias.

An experimental program is underway to further test inflation with more precise CMB measurements. In particular, high precision measurements of the so-called "B-modes" of the polarization of the background radiation could provide evidence of the gravitational radiation produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models (~ GeV) is correct. In March 2014, the BICEP2 team announced B-mode CMB polarization confirming inflation had been demonstrated. The team announced the tensor-to-scalar power ratio $k$ was between 0.15 and 0.27 (rejecting the null hypothesis; $3$ is expected to be 0 in the absence of inflation). However, on 19 June 2014, lowered confidence in confirming the findings was reported;  on 19 September 2014, a further reduction in confidence was reported  and, on 30 January 2015, even less confidence yet was reported. By 2018, additional data suggested, with 95% confidence, that $$r$$ is 0.06 or lower: consistent with the null hypothesis, but still also consistent with many remaining models of inflation.

Other potentially corroborating measurements are expected from the Planck spacecraft, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere. Other forthcoming measurements, such as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before the first stars formed), may measure the power spectrum with even greater resolution than the CMB and galaxy surveys, although it is not known if these measurements will be possible or if interference with radio sources on Earth and in the galaxy will be too great.

Theoretical status
In Guth's early proposal, it was thought that the inflaton was the Higgs field, the field that explains the mass of the elementary particles. It is now believed by some that the inflaton cannot be the Higgs field although the recent discovery of the Higgs boson has increased the number of works considering the Higgs field as inflaton. One problem of this identification is the current tension with experimental data at the electroweak scale, which is currently under study at the Large Hadron Collider (LHC). Other models of inflation relied on the properties of Grand Unified Theories. At present, while inflation is understood principally by its detailed predictions of the initial conditions for the hot early universe, the particle physics is largely ad hoc modelling. As such, although predictions of inflation have been consistent with the results of observational tests, many open questions remain.

Fine-tuning problem
One of the most severe challenges for inflation arises from the need for fine tuning. In new inflation, the slow-roll conditions must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton potential must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass. New inflation requires the Universe to have a scalar field with an especially flat potential and special initial conditions. However, explanations for these fine-tunings have been proposed. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied through perturbation theory.

Linde proposed a theory known as chaotic inflation in which he suggested that the conditions for inflation were actually satisfied quite generically. Inflation will occur in virtually any universe that begins in a chaotic, high energy state that has a scalar field with unbounded potential energy. However, in his model the inflaton field necessarily takes values larger than one Planck unit: for this reason, these are often called large field models and the competing new inflation models are called small field models. In this situation, the predictions of effective field theory are thought to be invalid, as renormalization should cause large corrections that could prevent inflation. This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models. While inflation depends on quantum field theory (and the semiclassical approximation to quantum gravity) in an important way, it has not been completely reconciled with these theories.

Brandenberger commented on fine-tuning in another situation. The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. This scale is suggested to be around GeV or  times the Planck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a hierarchy problem): the energy density given by the scalar potential is down by compared to the Planck density. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification.

Eternal inflation
In many models, the inflationary phase of the Universe's expansion lasts forever in at least some regions of the Universe. This occurs because inflating regions expand very rapidly, reproducing themselves. Unless the rate of decay to the non-inflating phase is sufficiently fast, new inflating regions are produced more rapidly than non-inflating regions. In such models, most of the volume of the Universe is continuously inflating at any given time.

All models of eternal inflation produce an infinite, hypothetical multiverse, typically a fractal. The multiverse theory has created significant dissension in the scientific community about the viability of the inflationary model.

Paul Steinhardt, one of the original architects of the inflationary model, introduced the first example of eternal inflation in 1983. He showed that the inflation could proceed forever by producing bubbles of non-inflating space filled with hot matter and radiation surrounded by empty space that continues to inflate. The bubbles could not grow fast enough to keep up with the inflation. Later that same year, Alexander Vilenkin showed that eternal inflation is generic.

Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes lift it to previous levels. These regions in which the inflaton fluctuates upwards expand much faster than regions in which the inflaton has a lower potential energy, and tend to dominate in terms of physical volume. It has been shown that any inflationary theory with an unbounded potential is eternal. There are well-known theorems that this steady state cannot continue forever into the past. Inflationary spacetime, which is similar to de Sitter space, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space collapse to form a gravitational singularity, a point where densities become infinite. Therefore, it is necessary to have a theory for the Universe's initial conditions.

In eternal inflation, regions with inflation have an exponentially growing volume, while regions that are not inflating don't. This suggests that the volume of the inflating part of the Universe in the global picture is always unimaginably larger than the part that has stopped inflating, even though inflation eventually ends as seen by any single pre-inflationary observer. Scientists disagree about how to assign a probability distribution to this hypothetical anthropic landscape. If the probability of different regions is counted by volume, one should expect that inflation will never end or applying boundary conditions that a local observer exists to observe it, that inflation will end as late as possible.

Some physicists believe this paradox can be resolved by weighting observers by their pre-inflationary volume. Others believe that there is no resolution to the paradox and that the multiverse is a critical flaw in the inflationary paradigm. Paul Steinhardt, who first introduced the eternal inflationary model, later became one of its most vocal critics for this reason.

Initial conditions
Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin. These models propose that while the Universe, on the largest scales, expands exponentially it was, is and always will be, spatially infinite and has existed, and will exist, forever.

Other proposals attempt to describe the ex nihilo creation of the Universe based on quantum cosmology and the following inflation. Vilenkin put forth one such scenario. Hartle and Hawking offered the no-boundary proposal for the initial creation of the Universe in which inflation comes about naturally.

Guth described the inflationary universe as the "ultimate free lunch": new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) the first law of thermodynamics (energy conservation) and the second law of thermodynamics (entropy and the arrow of time problem). However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by a quantum fluctuation. Don Page was an outspoken critic of inflation because of this anomaly. He stressed that the thermodynamic arrow of time necessitates low entropy initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase.

Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle–Hawking initial state. Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the Universe. However, Albrecht and Lorenzo Sorbo argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state is much higher than that of a non-inflationary cosmos. This is because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than that for a non-inflationary alternative, which outweighs any entropic considerations.

Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects. Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations that have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. Some disagreement remains about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable.

Hybrid inflation
Another kind of inflation, called hybrid inflation, is an extension of new inflation. It introduces additional scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state.

In hybrid inflation, one scalar field is responsible for most of the energy density (thus determining the rate of expansion), while another is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore, hybrid inflation is not eternal. When the second (slow-rolling) inflaton reaches the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the inflaton down its potential, leading to termination of inflation.

Relation to dark energy
Dark energy is broadly similar to inflation and is thought to be causing the expansion of the present-day universe to accelerate. However, the energy scale of dark energy is much lower, GeV, roughly 27 orders of magnitude less than the scale of inflation.

Inflation and string cosmology
The discovery of flux compactifications opened the way for reconciling inflation and string theory. Brane inflation suggests that inflation arises from the motion of D-branes in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the Dirac–Born–Infeld action, is different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in the string landscape. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism.

Inflation and loop quantum gravity
When investigating the effects the theory of loop quantum gravity would have on cosmology, a loop quantum cosmology model has evolved that provides a possible mechanism for cosmological inflation. Loop quantum gravity assumes a quantized spacetime. If the energy density is larger than can be held by the quantized spacetime, it is thought to bounce back.

Alternatives and adjuncts
Other models have been advanced that are claimed to explain some or all of the observations addressed by inflation.

Big bounce
The big bounce hypothesis attempts to replace the cosmic singularity with a cosmic contraction and bounce, thereby explaining the initial conditions that led to the big bang. The flatness and horizon problems are naturally solved in the Einstein–Cartan–Sciama–Kibble theory of gravity, without needing an exotic form of matter or free parameters. This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after the Big Bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era.

Ekpyrotic and cyclic models
The ekpyrotic and cyclic models are also considered adjuncts to inflation. These models solve the horizon problem through an expanding epoch well before the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a Big Crunch. The Universe passes through the Big Crunch and emerges in a hot Big Bang phase. In this sense they are reminiscent of Richard Chace Tolman's oscillatory universe; in Tolman's model, however, the total age of the Universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the Universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. Ekpyrotic models avoid the magnetic monopole problem as long as the temperature at the Big Crunch/Big Bang transition remains below the Grand Unified Scale, as this is the temperature required to produce magnetic monopoles in the first place. As things stand, there is no evidence of any 'slowing down' of the expansion, but this is not surprising as each cycle is expected to last on the order of a trillion years.

String gas cosmology
String theory requires that, in addition to the three observable spatial dimensions, additional dimensions exist that are curled up or compactified (see also Kaluza–Klein theory). Extra dimensions appear as a frequent component of supergravity models and other approaches to quantum gravity. This raised the contingent question of why four space-time dimensions became large and the rest became unobservably small. An attempt to address this question, called string gas cosmology, was proposed by Robert Brandenberger and Cumrun Vafa. This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension of spacetime can only expand if the strings that wind around it can efficiently annihilate each other. Each string is a one-dimensional object, and the largest number of dimensions in which two strings will generically intersect (and, presumably, annihilate) is three. Therefore, the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations. The original model did not "solve the entropy and flatness problems of standard cosmology", although Brandenburger and coauthors later argued that these problems can be eliminated by implementing string gas cosmology in the context of a bouncing-universe scenario.

Varying c
Cosmological models employing a variable speed of light have been proposed to resolve the horizon problem of and provide an alternative to cosmic inflation. In the VSL models, the fundamental constant c, denoting the speed of light in vacuum, is greater in the early universe than its present value, effectively increasing the particle horizon at the time of decoupling sufficiently to account for the observed isotropy of the CMB.

Criticisms
Since its introduction by Alan Guth in 1980, the inflationary paradigm has become widely accepted. Nevertheless, many physicists, mathematicians, and philosophers of science have voiced criticisms, claiming untestable predictions and a lack of serious empirical support. In 1999, John Earman and Jesús Mosterín published a thorough critical review of inflationary cosmology, concluding,
 * "we do not think that there are, as yet, good grounds for admitting any of the models of inflation into the standard core of cosmology."

As pointed out by Roger Penrose from 1986 on, in order to work, inflation requires extremely specific initial conditions of its own, so that the problem (or pseudo-problem) of initial conditions is not solved:
 * "There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process. ... For, if the thermalization is actually doing anything ... then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after."

The problem of specific or "fine-tuned" initial conditions would not have been solved; it would have gotten worse. At a conference in 2015, Penrose said that
 * "inflation isn't falsifiable, it's falsified. ... BICEP did a wonderful service by bringing all the Inflation-ists out of their shell, and giving them a black eye."

A recurrent criticism of inflation is that the invoked inflaton field does not correspond to any known physical field, and that its potential energy curve seems to be an ad hoc contrivance to accommodate almost any data obtainable. Paul Steinhardt, one of the founding fathers of inflationary cosmology, has recently become one of its sharpest critics. He calls 'bad inflation' a period of accelerated expansion whose outcome conflicts with observations, and 'good inflation' one compatible with them: Together with Anna Ijjas and Abraham Loeb, he wrote articles claiming that the inflationary paradigm is in trouble in view of the data from the Planck satellite.
 * "Not only is bad inflation more likely than good inflation, but no inflation is more likely than either ... Roger Penrose considered all the possible configurations of the inflaton and gravitational fields. Some of these configurations lead to inflation ... Other configurations lead to a uniform, flat universe directly – without inflation. Obtaining a flat universe is unlikely overall. Penrose's shocking conclusion, though, was that obtaining a flat universe without inflation is much more likely than with inflation – by a factor of 10 to the googol power!"

Counter-arguments were presented by Alan Guth, David Kaiser, and Yasunori Nomura and by Andrei Linde, saying that
 * "cosmic inflation is on a stronger footing than ever before".

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Inflation (cosmology)


text:
Talk:Physical cosmology

Update the main image of the CMB?
Wouldn't it make sense to update the main image of the CMB? The current image is the older and lower resolution WMAP image. The newer image, released in 2013, is the more scientifically up-to-date image. see below for NYT comparison: http://www.nytimes.com/interactive/2013/03/21/science/space/0321-universe.html?_r=0 Speedplane (talk) 17:14, 15 December 2014 (UTC)

Other cosmologies reference
J. V. Narlikar, Introduction to Cosmology, Jones and Bartlett Publishers, Inc., Boston, MA, 1983.(HCPotter (talk) 09:32, 12 February 2012 (UTC))

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Question
Wondering what is the difference between 'Physical cosmology' and 'Cosmic evolution'? I am thinking 'physical cosmology' is the study of the material aspects of the cosmos (which includes our universe, and all other billions & billions of universes) and all the stuff in it -- matter, energy, and it might include the subject of 'cosmic evolution', that is, how all this material stuff evolved? Or, is 'cosmic evolution' a separate area of study?--Tomwsulcer (talk) 23:25, 1 September 2014 (UTC)

"Excellent agreement with observations"
Should this phrase be removed: "which are in excellent agreement with many diverse observations." First, it lacks attribution. Secondly, because dark matter and dark entities are hypothetical entities introduced specifically to explain such observations, of course they will agree with those observations. Thus, just as WP is designed to prevent circularity in its own editing (i.e., WP articles may not reference each other for attribution), so too, if there is any circularity here, it will undermine the value of this article. Bob Enyart, Denver KGOV radio host (talk) 16:56, 5 September 2014 (UTC)

 * You seem to have posted the same thing twice. (Saw you fixed that -- thanks!)  The "excellent agreement" sentence in the lead should be a summary of more extensive material in the body of the article.  As such, it wouldn't ordinarily need separate sourcing.  However, it might be appropriate to give an attribution in the lead given that the development of the body does seem to be lacking in some areas.  We could add a citation of a review article or standard reference such as the PDG.  Your second point is not really correct (there are many different observational tests, and in many cases successful predictions rather than just post hoc model-fitting); and it's also not relevant to the article without outside sourcing for the argument. --Amble (talk) 19:38, 5 September 2014 (UTC)
 * For some examples: dark matter is inferred from local observations of galaxies and galaxy clusters. Dark energy is inferred from supernovae at z<2 or so.  When these are found to agree with cosmological data such as precision measurements of the CMB temperature power spectrum at z=1100, that agreement is far from trivial. --Amble (talk) 18:53, 6 September 2014 (UTC)
 * I've added the PDG citation. What do you think? --Amble (talk) 19:05, 6 September 2014 (UTC)

Discussion of capitalization of universe
There is request for comment about capitalization of the word universe at Wikipedia talk:Manual of Style/Capital letters. Please participate. SchreiberBike talk 00:44, 4 February 2015 (UTC)

Notification of request for comment
An RfC has been commenced at MOSCAPS Request for comment - Capitalise universe.

Cinderella157 (talk) 03:23, 22 March 2015 (UTC)

Slipher's conclusion
Regarding this sentence:

 * In the 1910s, Vesto Slipher (and later Carl Wilhelm Wirtz) interpreted the red shift of spiral nebulae as a Doppler shift that indicated they were receding from Earth.

I looked at a presentation by Slipher in 1917 and his conclusion then was as follows:

 * "We may in a like manner determine our motion relative to the spiral nebulæ, when sufficient material becomes available. A preliminary solution of the material at present available indicates that we are moving in the direction of right-ascension 22 hours and declination −22° with a velocity of about 700 km."

That is, as of 1917 he had not reached the conclusion as stated above, but instead suggested the redshift was due to the general motion of the Milky Way relative to the other nebulæ. The true interpretation came later, but it's not clear that happened during the 1910s. Praemonitus (talk) 22:51, 16 June 2015 (UTC)

 * I performed some more checking. This 1918 article appears to show that he was changing his views. By 1922 his findings showed that the velocities of the spiral nebulæ showed they were almost all moving away. I'm going to add the last as the reference. Praemonitus (talk) 15:53, 17 June 2015 (UTC)

 * The original statement from the article is slightly vague, depending on whether you take "spiral nebulae" to mean "some spiral nebulae, those which he had observed, primarily in one region of the sky", or "spiral nebulae as a general class". The main thing to clearly state is that Slipher already measured redshifts and used them to find relative velocities, most of which were receding; too often all of this gets credited to Hubble along with his later work.  Looks like your new reference is a good addition. --Amble (talk) 20:46, 17 June 2015 (UTC)

More cites needed in "Areas of Study"
The only inline citations now are for a debunked observation and the new subsection on gravitational waves. More are need in other paragraphs, especially for theoretical proposals and ideas. Layzeeboi (talk) 20:16, 31 March 2017 (UTC)
 * I've attempted to address this concern by adding many new references to the section. If there are still issues, inline tags can be used. Praemonitus (talk) 22:32, 11 April 2018 (UTC)
 * Nice work on improving the sourcing of this section. I concur that any remaining issues could be addressed with inline tags. --Mark viking (talk) 22:45, 11 April 2018 (UTC)

Main image caption needs to be rewritten
The main image caption says humanity is a red supernova, the internet is its core, and we live in the event horizon of a black hole. — Preceding unsigned comment added by 2600:8807:5601:8900:F061:21E7:222E:16D1 (talk) 16:49, 17 December 2018 (UTC)
 * Mmm, no. Praemonitus (talk) 17:58, 17 December 2018 (UTC)

Requested move 13 January 2022

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: withdrawn, will reformulate. (non-admin closure) Heanor (talk) 15:06, 13 January 2022 (UTC)

– Cosmology looks now as an attempt for a WP:broad-concept article. But I do not think that a broad-concept article on this topic is possible. it is definetly fails "expert test": the expert on "cosmology" would need to have both physics and religiom in their knowledge base, along with philosophy. From three main meaning of 'cosmology', the physical cosmology is the primary topic. Heanor (talk) 14:32, 13 January 2022 (UTC)
 * Physical cosmology → Cosmology
 * Cosmology → History of cosmology
 * Oppose: historically, cosmology began as a philosophical topic. The scientific study is a sub-topic of a broader theme. Praemonitus (talk) 14:56, 13 January 2022 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

'Physical Cosmology'
Of all the sources listed here, only a single one mentions the term 'physical cosmology', and it disagrees with this page on what physical cosmology is. arxiv:0602280 ,

"Cosmology is the study of the large-scale structure of the Universe, where ‘the Universe’ means all that exists in a physical sense [104]. This is to be distinguished from the Observable Universe, namely that part of the Universe containing matter accessible to our astronomical observations, which is a subset of the Universe proper. Thus cosmology considers the vast domain of galaxies, clusters of galaxies, quasi-stellar objects, etc., observable in the sky by use of telescopes of all kinds, examining their nature, distribution, origins, and relation to their larger environment. Observational cosmology [114, 128, 99, 189, 18] aims to determine the large-scale geometry of the observable universe and the distribution of matter in it from observations of radiation emitted by distant objects, while physical cosmology [163, 193, 233, 202, 171, 38] is the study of interactions during the expansion of the universe in its early hot big bang phase, and astrophysical cosmology [193, 165, 160, 174, 38] studies the resulting later development of large-scale structures such as galaxies and clusters of galaxies. "

What's listed on this page covers what this source refers to as Observational cosmology, physical cosmology and astrophysical cosmology, not just physical cosmology. Why has this article been renamed from what it is actually referred to as almost unanimously, to physical cosmology which it is almost never referred to as? 2001:56A:F343:2700:54C0:7516:B1C4:A703 (talk) 07:06, 20 March 2022 (UTC)
 * The content of this page is specifically focused on a branch of astronomy rather than metaphysics, so in the Wikipedia style it could alternatively be named Cosmology (astronomy) to distinguish it from Cosmology (metaphysics). Praemonitus (talk) 15:02, 20 March 2022 (UTC)
 * Cosmology (astronomy) would be better (since again, physical cosmology just is not what this field is called), though Cosmology (physics) would be better still since there are parts of cosmology that don't come under astronomy. 2001:56A:F343:2700:5DE7:8C70:11F5:1323 (talk) 16:37, 20 March 2022 (UTC)
 * Physics and astronomy are closely linked, but scientific cosmology is generally considered a field of astronomy (with elements of physics). I think Cosmology (physics) may be more confusing to people. Praemonitus (talk) 19:28, 20 March 2022 (UTC)
 * This isn't true, cosmology is not a field of astronomy. A lot of cosmology is part of astronomy, but not cosmology in general, there are parts of cosmology that are not astronomy. Cosmology (physics) would be the correct term. e.g. arXiv puts cosmology under the subheading physics, because cosmology is a subfield of physics. 2001:56A:F343:2700:5DE7:8C70:11F5:1323 (talk) 20:07, 20 March 2022 (UTC)
 * Article naming in Wikipedia is about what people expect to find when they do a lookup. Most people expect to find cosmology covered under astronomy. This is why there is a WP:COMMONNAME. Praemonitus (talk) 20:29, 20 March 2022 (UTC)
 * Yes this is why the article should be renamed to be what it is actually referred to, not the term it is called here which is not used. 2001:56A:F343:2700:5DE7:8C70:11F5:1323 (talk) 20:38, 20 March 2022 (UTC)
 * Well then we're at an impasse, because when I see "Cosmology (physics)" I immediately think "early Big Bang"; not the entire field of observational cosmology. Praemonitus (talk) 20:45, 20 March 2022 (UTC)
 * I'm not really sure why you think that as that isn't what the term means. Again, for example you can look through cosmology in the physics section of arXiv for one example of many, the vast majority is not just about the early Big Bang. 2001:56A:F343:2700:5DE7:8C70:11F5:1323 (talk) 21:42, 20 March 2022 (UTC)

title: Talk:Physical cosmology


text:
Candela

The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the luminous efficiency function, the model of the sensitivity of the human eye to different wavelengths, standardized by the CIE and ISO. A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.

The word candela is Latin for candle. The old name "candle" is still sometimes used, as in foot-candle and the modern definition of candlepower.

Definition
The 26th General Conference on Weights and Measures (CGPM) redefined the candela in 2018. The new definition, which took effect on 20 May 2019, is:

"The candela [...] is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency $1.02$. Kcd, to be 683 when expressed in the unit lm W−1, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs."

Explanation
The frequency chosen is in the visible spectrum near green, corresponding to a wavelength of about 555 nanometres. The human eye, when adapted for bright conditions, is most sensitive near this frequency. Under these conditions, photopic vision dominates the visual perception of our eyes over the scotopic vision. At other frequencies, more radiant intensity is required to achieve the same luminous intensity, according to the frequency response of the human eye. The luminous intensity for light of a particular wavelength λ is given by $$I_\mathrm{v}(\lambda)= 683.002\ \mathrm{lm/W} \cdot \overline{y}(\lambda) \cdot I_\mathrm{e}(\lambda) ,$$ where $I_{v}(λ)$ is the luminous intensity, $I_{e}(λ)$ is the radiant intensity and $\textstyle \overline{y}(\lambda)$ is the photopic luminous efficiency function. If more than one wavelength is present (as is usually the case), one must integrate over the spectrum of wavelengths to get the total luminous intensity.

Examples

 * A common candle emits light with roughly 1 cd luminous intensity.
 * A 25 W compact fluorescent light bulb puts out around 1700 lumens; if that light is radiated equally in all directions (i.e. over 4$\pi$ steradians), it will have an intensity of $$I_\text{V} = \frac{1700\ \text{lm}}{4 \pi\ \text{sr}} \approx 135\ \text{lm}/\text{sr} = 135\ \text{cd}.$$
 * Focused into a 20° beam (0.095 steradians), the same light bulb would have an intensity of around 18,000 cd within the beam.

History
Prior to 1948, various standards for luminous intensity were in use in a number of countries. These were typically based on the brightness of the flame from a "standard candle" of defined composition, or the brightness of an incandescent filament of specific design. One of the best-known of these was the English standard of candlepower. One candlepower was the light produced by a pure spermaceti candle weighing one sixth of a pound and burning at a rate of 120 grains per hour. Germany, Austria and Scandinavia used the Hefnerkerze, a unit based on the output of a Hefner lamp.

A better standard for luminous intensity was needed. In 1884, Jules Violle had proposed a standard based on the light emitted by 1 cm2 of platinum at its melting point (or freezing point). The resulting unit of intensity, called the "violle", was roughly equal to 60 English candlepower. Platinum was convenient for this purpose because it had a high enough melting point, was not prone to oxidation, and could be obtained in pure form. Violle showed that the intensity emitted by pure platinum was strictly dependent on its temperature, and so platinum at its melting point should have a consistent luminous intensity.

In practice, realizing a standard based on Violle's proposal turned out to be more difficult than expected. Impurities on the surface of the platinum could directly affect its emissivity, and in addition impurities could affect the luminous intensity by altering the melting point. Over the following half century various scientists tried to make a practical intensity standard based on incandescent platinum. The successful approach was to suspend a hollow shell of thorium dioxide with a small hole in it in a bath of molten platinum. The shell (cavity) serves as a black body, producing black-body radiation that depends on the temperature and is not sensitive to details of how the device is constructed.

In 1937, the Commission Internationale de l'Éclairage (International Commission on Illumination) and the CIPM proposed a "new candle" based on this concept, with value chosen to make it similar to the earlier unit candlepower. The decision was promulgated by the CIPM in 1946: "The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre."

It was then ratified in 1948 by the 9th CGPM which adopted a new name for this unit, the candela. In 1967 the 13th CGPM removed the term "new candle" and gave an amended version of the candela definition, specifying the atmospheric pressure applied to the freezing platinum: "The candela is the luminous intensity, in the perpendicular direction, of a surface of 1 / 600 000 square metre of a black body at the temperature of freezing platinum under a pressure of 101 325 newtons per square metre."

In 1979, because of the difficulties in realizing a Planck radiator at high temperatures and the new possibilities offered by radiometry, the 16th CGPM adopted a new definition of the candela:

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $1.11$ and that has a radiant intensity in that direction of $540,000,000,000,000 Hz$ watt per steradian.

The definition describes how to produce a light source that (by definition) emits one candela, but does not specify the luminous efficiency function for weighting radiation at other frequencies. Such a source could then be used to calibrate instruments designed to measure luminous intensity with reference to a specified luminous efficiency function. An appendix to the SI Brochure makes it clear that the luminous efficiency function is not uniquely specified, but must be selected to fully define the candela.

The arbitrary (1/683) term was chosen so that the new definition would precisely match the old definition. Although the candela is now defined in terms of the second (an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition.

The 26th CGPM approved the modern definition of the candela in 2018 as part of the 2019 redefinition of SI base units, which redefined the SI base units in terms of fundamental physical constants.

Relationships between luminous intensity, luminous flux, and illuminance
If a source emits a known luminous intensity $I_{v}$ (in candelas) in a well-defined cone, the total luminous flux $Φ_{v}$ in lumens is given by $$\Phi_\mathrm{v} = I_\mathrm{v} 2 \pi [1 - \cos(A/2)]$$ where $A$ is the radiation angle of the lamp—the full vertex angle of the emission cone. For example, a lamp that emits 590 cd with a radiation angle of 40° emits about 224 lumens. See MR16 for emission angles of some common lamps.

If the source emits light uniformly in all directions, the flux can be found by multiplying the intensity by 4π: a uniform 1 candela source emits 12.6 lumens.

For the purpose of measuring illumination, the candela is not a practical unit, as it only applies to idealized point light sources, each approximated by a source small compared to the distance from which its luminous radiation is measured, also assuming that it is done so in the absence of other light sources. What gets directly measured by a light meter is incident light on a sensor of finite area, i.e. illuminance in lm/m2 (lux). However, if designing illumination from many point light sources, like light bulbs, of known approximate omnidirectionally uniform intensities, the contributions to illuminance from incoherent light being additive, it is mathematically estimated as follows. If $r_{i}$ is the position of the ith source of uniform intensity $I_{i}$, and $â$ is the unit vector normal to the illuminated elemental opaque area $dA$ being measured, and provided that all light sources lie in the same half-space divided by the plane of this area, $$ \text{illuminance at point } \mathbf{r}\text{ on } dA\text{, } E_\mathrm v(\mathbf{r}) = \sum _{i}{ \frac{|\mathbf{\hat{a}}\cdot(\mathbf{r}-\mathbf{r}_i)|}{|\mathbf{r}-\mathbf{r}_i|^3} I_i }.$$ In the case of a single point light source of intensity Iv, at a distance r and normally incident, this reduces to $$ E_\mathrm{v} (r) = \frac{I_\mathrm v}{r^2}.$$

SI multiples
Like other SI units, the candela can also be modified by adding a metric prefix that multiplies it by a power of 10, for example millicandela (mcd) for 10−3 candela.

title: Candela


text:
Condensed matter physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics theories to develop mathematical models and predict the properties of extremely large groups of atoms.

The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists self-identify as condensed matter physicists, and the Division of Condensed Matter Physics is the largest division of the American Physical Society. These include solid state and soft matter physicists, who study quantum and non-quantum physical properties of matter respectively. Both types study a great range of materials, providing many research, funding and employment opportunities. The field overlaps with chemistry, materials science, engineering and nanotechnology, and relates closely to atomic physics and biophysics. The theoretical physics of condensed matter shares important concepts and methods with that of particle physics and nuclear physics.

A variety of topics in physics such as crystallography, metallurgy, elasticity, magnetism, etc., were treated as distinct areas until the 1940s, when they were grouped together as solid-state physics. Around the 1960s, the study of physical properties of liquids was added to this list, forming the basis for the more comprehensive specialty of condensed matter physics. The Bell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics. According to the founding director of the Max Planck Institute for Solid State Research, physics professor Manuel Cardona, it was Albert Einstein who created the modern field of condensed matter physics starting with his seminal 1905 article on the photoelectric effect and photoluminescence which opened the fields of photoelectron spectroscopy and photoluminescence spectroscopy, and later his 1907 article on the specific heat of solids which introduced, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular the specific heat. Deputy Director of the Yale Quantum Institute A. Douglas Stone makes a similar priority case for Einstein in his work on the synthetic history of quantum mechanics.

Etymology
According to physicist Philip Warren Anderson, the use of the term "condensed matter" to designate a field of study was coined by him and Volker Heine, when they changed the name of their group at the Cavendish Laboratories, Cambridge, from Solid state theory to Theory of Condensed Matter in 1967, as they felt it better included their interest in liquids, nuclear matter, and so on. Although Anderson and Heine helped popularize the name "condensed matter", it had been used in Europe for some years, most prominently in the Springer-Verlag journal Physics of Condensed Matter, launched in 1963. The name "condensed matter physics" emphasized the commonality of scientific problems encountered by physicists working on solids, liquids, plasmas, and other complex matter, whereas "solid state physics" was often associated with restricted industrial applications of metals and semiconductors. In the 1960s and 70s, some physicists felt the more comprehensive name better fit the funding environment and Cold War politics of the time.

References to "condensed" states can be traced to earlier sources. For example, in the introduction to his 1947 book Kinetic Theory of Liquids, Yakov Frenkel proposed that "The kinetic theory of liquids must accordingly be developed as a generalization and extension of the kinetic theory of solid bodies. As a matter of fact, it would be more correct to unify them under the title of 'condensed bodies.

Classical physics

One of the first studies of condensed states of matter was by English chemist Humphry Davy, in the first decades of the nineteenth century. Davy observed that of the forty chemical elements known at the time, twenty-six had metallic properties such as lustre, ductility and high electrical and thermal conductivity. This indicated that the atoms in John Dalton's atomic theory were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as nitrogen and hydrogen could be liquefied under the right conditions and would then behave as metals.

In 1823, Michael Faraday, then an assistant in Davy's lab, successfully liquefied chlorine and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and oxygen. Shortly after, in 1869, Irish chemist Thomas Andrews studied the phase transition from a liquid to a gas and coined the term critical point to describe the condition where a gas and a liquid were indistinguishable as phases, and Dutch physicist Johannes van der Waals supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures. By 1908, James Dewar and Heike Kamerlingh Onnes were successfully able to liquefy hydrogen and then newly discovered helium, respectively.

Paul Drude in 1900 proposed the first theoretical model for a classical electron moving through a metallic solid. Drude's model described properties of metals in terms of a gas of free electrons, and was the first microscopic model to explain empirical observations such as the Wiedemann–Franz law. However, despite the success of Drude's model, it had one notable problem: it was unable to correctly explain the electronic contribution to the specific heat and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures.

In 1911, three years after helium was first liquefied, Onnes working at University of Leiden discovered superconductivity in mercury, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value. The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades. Albert Einstein, in 1922, said regarding contemporary theories of superconductivity that "with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas."

Advent of quantum mechanics
Drude's classical model was augmented by Wolfgang Pauli, Arnold Sommerfeld, Felix Bloch and other physicists. Pauli realized that the free electrons in metal must obey the Fermi–Dirac statistics. Using this idea, he developed the theory of paramagnetism in 1926. Shortly after, Sommerfeld incorporated the Fermi–Dirac statistics into the free electron model and made it better to explain the heat capacity. Two years later, Bloch used quantum mechanics to describe the motion of an electron in a periodic lattice. The mathematics of crystal structures developed by Auguste Bravais, Yevgraf Fyodorov and others was used to classify crystals by their symmetry group, and tables of crystal structures were the basis for the series International Tables of Crystallography, first published in 1935. Band structure calculations was first used in 1930 to predict the properties of new materials, and in 1947 John Bardeen, Walter Brattain and William Shockley developed the first semiconductor-based transistor, heralding a revolution in electronics.

In 1879, Edwin Herbert Hall working at the Johns Hopkins University discovered a voltage developed across conductors transverse to an electric current in the conductor and magnetic field perpendicular to the current. This phenomenon arising due to the nature of charge carriers in the conductor came to be termed the Hall effect, but it was not properly explained at the time, since the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics, Lev Landau in 1930 developed the theory of Landau quantization and laid the foundation for the theoretical explanation for the quantum Hall effect discovered half a century later.

Magnetism as a property of matter has been known in China since 4000 BC. However, the first modern studies of magnetism only started with the development of electrodynamics by Faraday, Maxwell and others in the nineteenth century, which included classifying materials as ferromagnetic, paramagnetic and diamagnetic based on their response to magnetization. Pierre Curie studied the dependence of magnetization on temperature and discovered the Curie point phase transition in ferromagnetic materials. In 1906, Pierre Weiss introduced the concept of magnetic domains to explain the main properties of ferromagnets. The first attempt at a microscopic description of magnetism was by Wilhelm Lenz and Ernst Ising through the Ising model that described magnetic materials as consisting of a periodic lattice of spins that collectively acquired magnetization. The Ising model was solved exactly to show that spontaneous magnetization can occur in one dimension and it is possible in higher-dimensional lattices. Further research such as by Bloch on spin waves and Néel on antiferromagnetism led to developing new magnetic materials with applications to magnetic storage devices.

Modern many-body physics
The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of superconductivity and the Kondo effect. After World War II, several ideas from quantum field theory were applied to condensed matter problems. These included recognition of collective excitation modes of solids and the important notion of a quasiparticle. Soviet physicist Lev Landau used the idea for the Fermi liquid theory wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles. Landau also developed a mean-field theory for continuous phase transitions, which described ordered phases as spontaneous breakdown of symmetry. The theory also introduced the notion of an order parameter to distinguish between ordered phases. Eventually in 1956, John Bardeen, Leon Cooper and Robert Schrieffer developed the so-called BCS theory of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by phonons in the lattice can give rise to a bound state called a Cooper pair.

The study of phase transitions and the critical behavior of observables, termed critical phenomena, was a major field of interest in the 1960s. Leo Kadanoff, Benjamin Widom and Michael Fisher developed the ideas of critical exponents and widom scaling. These ideas were unified by Kenneth G. Wilson in 1972, under the formalism of the renormalization group in the context of quantum field theory.

The quantum Hall effect was discovered by Klaus von Klitzing, Dorda and Pepper in 1980 when they observed the Hall conductance to be integer multiples of a fundamental constant $$e^2/h$$.(see figure) The effect was observed to be independent of parameters such as system size and impurities. In 1981, theorist Robert Laughlin proposed a theory explaining the unanticipated precision of the integral plateau. It also implied that the Hall conductance is proportional to a topological invariant, called Chern number, whose relevance for the band structure of solids was formulated by David J. Thouless and collaborators. Shortly after, in 1982, Horst Störmer and Daniel Tsui observed the fractional quantum Hall effect where the conductance was now a rational multiple of the constant $$e^2/h$$. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a variational method solution, named the Laughlin wavefunction. The study of topological properties of the fractional Hall effect remains an active field of research. Decades later, the aforementioned topological band theory advanced by David J. Thouless and collaborators was further expanded leading to the discovery of topological insulators.

In 1986, Karl Müller and Johannes Bednorz discovered the first high temperature superconductor, La2-xBaxCuO4, which is superconducting at temperatures as high as 39 kelvin. It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role. A satisfactory theoretical description of high-temperature superconductors is still not known and the field of strongly correlated materials continues to be an active research topic.

In 2012, several groups released preprints which suggest that samarium hexaboride has the properties of a topological insulator in accord with the earlier theoretical predictions. Since samarium hexaboride is an established Kondo insulator, i.e. a strongly correlated electron material, it is expected that the existence of a topological Dirac surface state in this material would lead to a topological insulator with strong electronic correlations.

Theoretical
Theoretical condensed matter physics involves the use of theoretical models to understand properties of states of matter. These include models to study the electronic properties of solids, such as the Drude model, the band structure and the density functional theory. Theoretical models have also been developed to study the physics of phase transitions, such as the Ginzburg–Landau theory, critical exponents and the use of mathematical methods of quantum field theory and the renormalization group. Modern theoretical studies involve the use of numerical computation of electronic structure and mathematical tools to understand phenomena such as high-temperature superconductivity, topological phases, and gauge symmetries.

Emergence
Theoretical understanding of condensed matter physics is closely related to the notion of emergence, wherein complex assemblies of particles behave in ways dramatically different from their individual constituents. For example, a range of phenomena related to high temperature superconductivity are understood poorly, although the microscopic physics of individual electrons and lattices is well known. Similarly, models of condensed matter systems have been studied where collective excitations behave like photons and electrons, thereby describing electromagnetism as an emergent phenomenon. Emergent properties can also occur at the interface between materials: one example is the lanthanum aluminate-strontium titanate interface, where two band-insulators are joined to create conductivity and superconductivity.

Electronic theory of solids
The metallic state has historically been an important building block for studying properties of solids. The first theoretical description of metals was given by Paul Drude in 1900 with the Drude model, which explained electrical and thermal properties by describing a metal as an ideal gas of then-newly discovered electrons. He was able to derive the empirical Wiedemann-Franz law and get results in close agreement with the experiments. This classical model was then improved by Arnold Sommerfeld who incorporated the Fermi–Dirac statistics of electrons and was able to explain the anomalous behavior of the specific heat of metals in the Wiedemann–Franz law. In 1912, The structure of crystalline solids was studied by Max von Laue and Paul Knipping, when they observed the X-ray diffraction pattern of crystals, and concluded that crystals get their structure from periodic lattices of atoms. In 1928, Swiss physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, known as Bloch's theorem.

Calculating electronic properties of metals by solving the many-body wavefunction is often computationally hard, and hence, approximation methods are needed to obtain meaningful predictions. The Thomas–Fermi theory, developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a variational parameter. Later in the 1930s, Douglas Hartree, Vladimir Fock and John Slater developed the so-called Hartree–Fock wavefunction as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for exchange statistics of single particle electron wavefunctions. In general, it is very difficult to solve the Hartree–Fock equation. Only the free electron gas case can be solved exactly. Finally in 1964–65, Walter Kohn, Pierre Hohenberg and Lu Jeu Sham proposed the density functional theory (DFT) which gave realistic descriptions for bulk and surface properties of metals. The density functional theory has been widely used since the 1970s for band structure calculations of variety of solids.

Symmetry breaking
Some states of matter exhibit symmetry breaking, where the relevant laws of physics possess some form of symmetry that is broken. A common example is crystalline solids, which break continuous translational symmetry. Other examples include magnetized ferromagnets, which break rotational symmetry, and more exotic states such as the ground state of a BCS superconductor, that breaks U(1) phase rotational symmetry.

Goldstone's theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons. For example, in crystalline solids, these correspond to phonons, which are quantized versions of lattice vibrations.

Phase transition
Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such as temperature, pressure, or molar composition. In a single-component system, a classical phase transition occurs at a temperature (at a specific pressure) where there is an abrupt change in the order of the system   For example, when ice melts and becomes water, the ordered hexagonal crystal structure of ice is modified to a hydrogen bonded, mobile arrangement of water molecules.

In quantum phase transitions, the temperature is set to absolute zero, and the non-thermal control parameter, such as pressure or magnetic field,  causes the phase transitions when order is destroyed by quantum fluctuations originating from the Heisenberg uncertainty principle. Here, the different quantum phases of the system refer to distinct ground states of the Hamiltonian matrix. Understanding the behavior of quantum phase transition is important in the difficult tasks of explaining the properties of rare-earth magnetic insulators, high-temperature superconductors, and other substances.

Two classes of phase transitions occur: first-order transitions and second-order or continuous transitions. For the latter, the two phases involved do not co-exist at the transition temperature, also called the critical point. Near the critical point, systems undergo critical behavior, wherein several of their properties such as correlation length, specific heat, and magnetic susceptibility diverge exponentially. These critical phenomena present serious challenges to physicists because normal macroscopic laws are no longer valid in the region, and novel ideas and methods must be invented to find the new laws that can describe the system.

The simplest theory that can describe continuous phase transitions is the Ginzburg–Landau theory, which works in the so-called mean-field approximation. However, it can only roughly explain continuous phase transition for ferroelectrics and type I superconductors which involves long range microscopic interactions. For other types of systems that involves short range interactions near the critical point, a better theory is needed.

Near the critical point, the fluctuations happen over broad range of size scales while the feature of the whole system is scale invariant. Renormalization group methods successively average out the shortest wavelength fluctuations in stages while retaining their effects into the next stage. Thus, the changes of a physical system as viewed at different size scales can be investigated systematically. The methods, together with powerful computer simulation, contribute greatly to the explanation of the critical phenomena associated with continuous phase transition.

Experimental
Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects of electric and magnetic fields, measuring response functions, transport properties and thermometry. Commonly used experimental methods include spectroscopy, with probes such as X-rays, infrared light and inelastic neutron scattering; study of thermal response, such as specific heat and measuring transport via thermal and heat conduction.

Scattering
Several condensed matter experiments involve scattering of an experimental probe, such as X-ray, optical photons, neutrons, etc., on constituents of a material. The choice of scattering probe depends on the observation energy scale of interest. Visible light has energy on the scale of 1 electron volt (eV) and is used as a scattering probe to measure variations in material properties such as the dielectric constant and refractive index. X-rays have energies of the order of 10 keV and hence are able to probe atomic length scales, and are used to measure variations in electron charge density and crystal structure.

Neutrons can also probe atomic length scales and are used to study the scattering off nuclei and electron spins and magnetization (as neutrons have spin but no charge). Coulomb and Mott scattering measurements can be made by using electron beams as scattering probes. Similarly, positron annihilation can be used as an indirect measurement of local electron density. Laser spectroscopy is an excellent tool for studying the microscopic properties of a medium, for example, to study forbidden transitions in media with nonlinear optical spectroscopy.

External magnetic fields
In experimental condensed matter physics, external magnetic fields act as thermodynamic variables that control the state, phase transitions and properties of material systems. Nuclear magnetic resonance (NMR) is a method by which external magnetic fields are used to find resonance modes of individual nuclei, thus giving information about the atomic, molecular, and bond structure of their environment. NMR experiments can be made in magnetic fields with strengths up to 60 tesla. Higher magnetic fields can improve the quality of NMR measurement data. Quantum oscillations is another experimental method where high magnetic fields are used to study material properties such as the geometry of the Fermi surface. High magnetic fields will be useful in experimental testing of the various theoretical predictions such as the quantized magnetoelectric effect, image magnetic monopole, and the half-integer quantum Hall effect.

Magnetic resonance spectroscopy
The local structure, as well as the structure of the nearest neighbour atoms, can be investigated in condensed matter with magnetic resonance methods, such as electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR), which are very sensitive to the details of the surrounding of nuclei and electrons by means of the hyperfine coupling. Both localized electrons and specific stable or unstable isotopes of the nuclei become the probe of these hyperfine interactions), which couple the electron or nuclear spin to the local electric and magnetic fields. These methods are suitable to study defects, diffusion, phase transitions and magnetic order. Common experimental methods include NMR, nuclear quadrupole resonance (NQR), implanted radioactive probes as in the case of muon spin spectroscopy ($$ \mu$$SR), Mössbauer spectroscopy, $$\beta$$NMR and perturbed angular correlation (PAC). PAC is especially ideal for the study of phase changes at extreme temperatures above 2000 °C due to the temperature independence of the method.

Cold atomic gases

Ultracold atom trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and in atomic, molecular, and optical physics. The method involves using optical lasers to form an interference pattern, which acts as a lattice, in which ions or atoms can be placed at very low temperatures. Cold atoms in optical lattices are used as quantum simulators, that is, they act as controllable systems that can model behavior of more complicated systems, such as frustrated magnets. In particular, they are used to engineer one-, two- and three-dimensional lattices for a Hubbard model with pre-specified parameters, and to study phase transitions for antiferromagnetic and spin liquid ordering.

In 1995, a gas of rubidium atoms cooled down to a temperature of 170 nK was used to experimentally realize the Bose–Einstein condensate, a novel state of matter originally predicted by S. N. Bose and Albert Einstein, wherein a large number of atoms occupy one quantum state.

Applications

Research in condensed matter physics has given rise to several device applications, such as the development of the semiconductor transistor, laser technology, magnetic storage, liquid crystals, optical fibres and several phenomena studied in the context of nanotechnology. Methods such as scanning-tunneling microscopy can be used to control processes at the nanometer scale, and have given rise to the study of nanofabrication. Such molecular machines were developed for example by Nobel laurates in chemistry Ben Feringa, Jean-Pierre Sauvage and Fraser Stoddart. Feringa and his team developed multiple molecular machines such as the molecular car, molecular windmill and many more.

In quantum computation, information is represented by quantum bits, or qubits. The qubits may decohere quickly before useful computation is completed. This serious problem must be solved before quantum computing may be realized. To solve this problem, several promising approaches are proposed in condensed matter physics, including Josephson junction qubits, spintronic qubits using the spin orientation of magnetic materials, or the topological non-Abelian anyons from fractional quantum Hall effect states.

Condensed matter physics also has important uses for biomedicine, for example, the experimental method of magnetic resonance imaging, which is widely used in medical diagnosis.

title: Condensed matter physics