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Hubble's law

Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible light spectrum. The discovery of Hubble's law is attributed to Edwin Hubble's work published in 1929.

Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model. The motion of astronomical objects due solely to this expansion is known as the Hubble flow. It is described by the equation $v = H_{0}D$, with $H_{0}$ the constant of proportionality—the Hubble constant—between the "proper distance" $D$ to a galaxy (which can change over time, unlike the comoving distance) and its speed of separation $v$, i.e. the derivative of proper distance with respect to the cosmic time coordinate. (See  for discussion of the subtleties of this definition of velocity.)

The Hubble constant is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy 1 Mpc away, and its value is about 70 (km/s)/Mpc. However, crossing out units reveals that $H_{0}$ is a unit of frequency (SI unit: s−1) and the reciprocal of $H_{0}$ is known as the Hubble time. The Hubble constant can also be interpreted as the relative rate of expansion. In this form $H_{0}$ = 7%/Gyr, meaning that at the current rate of expansion it takes a billion years for an unbound structure to grow by 7%.

Although widely attributed to Edwin Hubble,  the notion of the universe expanding at a calculable rate was first derived from general relativity equations in 1922 by Alexander Friedmann. Friedmann published a set of equations, now known as the Friedmann equations, showing that the universe might be expanding, and presenting the expansion speed if that were the case. Before Hubble, German astronomer Carl Wilhelm Wirtz had, in two publications dating 1922 and 1924, already deduced with his own data that galaxies that appeared smaller and dimmer had larger redshifts and thus that more distance galaxies recede faster from the observer. Then Georges Lemaître, in a 1927 article, independently derived that the universe might be expanding, observed the proportionality between recessional velocity of, and distance to, distant bodies, and suggested an estimated value for the proportionality constant; this constant, when Edwin Hubble confirmed the existence of cosmic expansion and determined a more accurate value for it two years later, came to be known by his name as the Hubble constant. Hubble inferred the recession velocity of the objects from their redshifts, many of which were earlier measured and related to velocity by Vesto Slipher in 1917. Combining Slipher's velocities with Henrietta Swan Leavitt's intergalactic distance calculations and methodology allowed Hubble to better calculate an expansion rate for the universe.

Though the Hubble constant $H_{0}$ is constant at any given moment in time, the Hubble parameter $H$, of which the Hubble constant is the current value, varies with time, so the term constant is sometimes thought of as somewhat of a misnomer.

Discovery

A decade before Hubble made his observations, a number of physicists and mathematicians had established a consistent theory of an expanding universe by using Einstein field equations of general relativity. Applying the most general principles to the nature of the universe yielded a dynamic solution that conflicted with the then-prevalent notion of a static universe.

Slipher's observations
In 1912, Vesto M. Slipher measured the first Doppler shift of a "spiral nebula" (the obsolete term for spiral galaxies) and soon discovered that almost all such nebulae were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was highly controversial whether or not these nebulae were "island universes" outside the Milky Way galaxy.

FLRW equations
In 1922, Alexander Friedmann derived his Friedmann equations from Einstein field equations, showing that the universe might expand at a rate calculable by the equations. The parameter used by Friedmann is known today as the scale factor and can be considered as a scale invariant form of the proportionality constant of Hubble's law. Georges Lemaître independently found a similar solution in his 1927 paper discussed in the following section. The Friedmann equations are derived by inserting the metric for a homogeneous and isotropic universe into Einstein's field equations for a fluid with a given density and pressure. This idea of an expanding spacetime would eventually lead to the Big Bang and Steady State theories of cosmology.

Lemaître's equation
In 1927, two years before Hubble published his own article, the Belgian priest and astronomer Georges Lemaître was the first to publish research deriving what is now known as Hubble's law. According to the Canadian astronomer Sidney van den Bergh, "the 1927 discovery of the expansion of the universe by Lemaître was published in French in a low-impact journal. In the 1931 high-impact English translation of this article, a critical equation was changed by omitting reference to what is now known as the Hubble constant." It is now known that the alterations in the translated paper were carried out by Lemaître himself.

Shape of the universe
Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe. In 1920, the Shapley–Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy, and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations.

Cepheid variable stars outside the Milky Way
Edwin Hubble did most of his professional astronomical observing work at Mount Wilson Observatory, home to the world's most powerful telescope at the time. His observations of Cepheid variable stars in "spiral nebulae" enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. They continued to be called nebulae, and it was only gradually that the term galaxies replaced it.

Combining redshifts with distance measurements

The parameters that appear in Hubble's law, velocities and distances, are not directly measured. In reality we determine, say, a supernova brightness, which provides information about its distance, and the redshift $H_{0}$ of its spectrum of radiation. Hubble correlated brightness and parameter $z$.

Combining his measurements of galaxy distances with Vesto Slipher and Milton Humason's measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality between redshift of an object and its distance. Though there was considerable scatter (now known to be caused by peculiar velocities—the 'Hubble flow' is used to refer to the region of space far enough out that the recession velocity is larger than local peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500 (km/s)/Mpc (much higher than the currently accepted value due to errors in his distance calibrations; see cosmic distance ladder for details).

Hubble diagram
Hubble's law can be easily depicted in a "Hubble diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer. A straight line of positive slope on this diagram is the visual depiction of Hubble's law.

Cosmological constant abandoned
After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant, which he had designed to modify his equations of general relativity to allow them to produce a static solution, which he thought was the correct state of the universe. The Einstein equations in their simplest form model either an expanding or contracting universe, so Einstein's cosmological constant was artificially created to counter the expansion or contraction to get a perfect static and flat universe. After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that the universe is static his "biggest mistake". On its own, general relativity could predict the expansion of the universe, which (through observations such as the bending of light by large masses, or the precession of the orbit of Mercury) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.

In 1931, Einstein went to Mount Wilson Observatory to thank Hubble for providing the observational basis for modern cosmology.

The cosmological constant has regained attention in recent decades as a hypothetical explanation for dark energy.

Interpretation
The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation between recessional velocity and redshift, yields a straightforward mathematical expression for Hubble's law as follows:

$$v = H_0 \, D$$

where
 * $v$ is the recessional velocity, typically expressed in km/s.
 * $H_{0}$ is Hubble's constant and corresponds to the value of $H$ (often termed the Hubble parameter which is a value that is time dependent and which can be expressed in terms of the scale factor) in the Friedmann equations taken at the time of observation denoted by the subscript $H_{0}$. This value is the same throughout the universe for a given comoving time.
 * $D$ is the proper distance (which can change over time, unlike the comoving distance, which is constant) from the galaxy to the observer, measured in mega parsecs (Mpc), in the 3-space defined by given cosmological time. (Recession velocity is just $z = ∆λ/λ$).

Hubble's law is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted and is not established except for small redshifts.

For distances $D$ larger than the radius of the Hubble sphere $v = cz$, objects recede at a rate faster than the speed of light (See Uses of the proper distance for a discussion of the significance of this):

$$r_\text{HS} = \frac{c}{H_0} \. $$

Since the Hubble "constant" is a constant only in space, not in time, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today. Current evidence suggests that the expansion of the universe is accelerating (see Accelerating universe), meaning that for any given galaxy, the recession velocity $dD/dt$ is increasing over time as the galaxy moves to greater and greater distances; however, the Hubble parameter is actually thought to be decreasing with time, meaning that if we were to look at some distance $D$ and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones.

Redshift velocity and recessional velocity
Redshift can be measured by determining the wavelength of a known transition, such as hydrogen α-lines for distant quasars, and finding the fractional shift compared to a stationary reference. Thus, redshift is a quantity unambiguous for experimental observation. The relation of redshift to recessional velocity is another matter.

Redshift velocity
The redshift $z$ is often described as a redshift velocity, which is the recessional velocity that would produce the same redshift it were caused by a linear Doppler effect (which, however, is not the case, as the shift is caused in part by a cosmological expansion of space, and because the velocities involved are too large to use a non-relativistic formula for Doppler shift). This redshift velocity can easily exceed the speed of light. In other words, to determine the redshift velocity $H_{0}$, the relation:

$$ v_\text{rs} \equiv cz,$$

is used. That is, there is between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-called Fizeau–Doppler formula

$$z = \frac{\lambda_\text{o}}{\lambda_\text{e}}-1 = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}-1 \approx \frac{v}{c}.$$

Here, $0$, $v = dD/dt$ are the observed and emitted wavelengths respectively. The "redshift velocity" $r_{HS}$ is not so simply related to real velocity at larger velocities, however, and this terminology leads to confusion if interpreted as a real velocity. Next, the connection between redshift or redshift velocity and recessional velocity is discussed.

Recessional velocity
Suppose $v_{rs}$ is called the scale factor of the universe, and increases as the universe expands in a manner that depends upon the cosmological model selected. Its meaning is that all measured proper distances $λ_{o}$ between co-moving points increase proportionally to $R$. (The co-moving points are not moving relative to each other except as a result of the expansion of space.) In other words:

$$\frac {D(t)}{D(t_0)} = \frac{R(t)}{R(t_0)},$$

where $λ_{e}$ is some reference time. If light is emitted from a galaxy at time $v_{rs}$ and received by us at $R(t)$, it is redshifted due to the expansion of space, and this redshift $z$ is simply:

$$z = \frac {R(t_0)}{R(t_\text{e})} - 1. $$

Suppose a galaxy is at distance $D$, and this distance changes with time at a rate $d_{t}D$. We call this rate of recession the "recession velocity" $D(t)$:

$$v_\text{r} = d_tD = \frac {d_tR}{R} D. $$

We now define the Hubble constant as

$$H \equiv \frac{d_tR}{R}, $$

and discover the Hubble law:

$$ v_\text{r} = H D. $$

From this perspective, Hubble's law is a fundamental relation between (i) the recessional velocity contributed by the expansion of space and (ii) the distance to an object; the connection between redshift and distance is a crutch used to connect Hubble's law with observations. This law can be related to redshift $z$ approximately by making a Taylor series expansion:

$$ z = \frac {R(t_0)}{R(t_e)} - 1 \approx \frac {R(t_0)} {R(t_0)\left(1+(t_e-t_0)H(t_0)\right)}-1 \approx (t_0-t_e)H(t_0), $$

If the distance is not too large, all other complications of the model become small corrections, and the time interval is simply the distance divided by the speed of light:

$$ z \approx (t_0-t_\text{e})H(t_0) \approx \frac {D}{c} H(t_0), $$

or

$$ cz \approx D H(t_0) = v_r. $$

According to this approach, the relation cz = vr is an approximation valid at low redshifts, to be replaced by a relation at large redshifts that is model-dependent. See velocity-redshift figure.

Observability of parameters
Strictly speaking, neither $v$ nor $D$ in the formula are directly observable, because they are properties of a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it.

For relatively nearby galaxies (redshift $z$ much less than unity), $v$ and $D$ will not have changed much, and $v$ can be estimated using the formula $t_{0}$ where $c$ is the speed of light. This gives the empirical relation found by Hubble.

For distant galaxies, $v$ (or $D$) cannot be calculated from $z$ without specifying a detailed model for how $H$ changes with time. The redshift is not even directly related to the recession velocity at the time the light set out, but it does have a simple interpretation: $t_{e}$ is the factor by which the universe has expanded while the photon was traveling towards the observer.

Expansion velocity vs. peculiar velocity
In using Hubble's law to determine distances, only the velocity due to the expansion of the universe can be used. Since gravitationally interacting galaxies move relative to each other independent of the expansion of the universe, these relative velocities, called peculiar velocities, need to be accounted for in the application of Hubble's law. Such peculiar velocities give rise to redshift-space distortions.

Time-dependence of Hubble parameter
The parameter $H$ is commonly called the "Hubble constant", but that is a misnomer since it is constant in space only at a fixed time; it varies with time in nearly all cosmological models, and all observations of far distant objects are also observations into the distant past, when the "constant" had a different value. "Hubble parameter" is a more correct term, with $t_{0}$ denoting the present-day value.

Another common source of confusion is that the accelerating universe does imply that the Hubble parameter is actually increasing with time; since $ H(t) \equiv \dot{a}(t)/a(t) $, in most accelerating models $$a$$ increases relatively faster than $\dot{a}$, so $H$ decreases with time. (The recession velocity of one chosen galaxy does increase, but different galaxies passing a sphere of fixed radius cross the sphere more slowly at later times.)

On defining the dimensionless deceleration parameter $ q \equiv - \frac {\ddot{a}\, a} {\dot{a}^2} $, it follows that

$$ \frac{dH}{dt} = -H^2 (1+q) $$

From this it is seen that the Hubble parameter is decreasing with time, unless $v_{r}$; the latter can only occur if the universe contains phantom energy, regarded as theoretically somewhat improbable.

However, in the standard Lambda cold dark matter model (Lambda-CDM or ΛCDM model), $q$ will tend to −1 from above in the distant future as the cosmological constant becomes increasingly dominant over matter; this implies that $H$ will approach from above to a constant value of ≈ 57 (km/s)/Mpc, and the scale factor of the universe will then grow exponentially in time.

Idealized Hubble's law
The mathematical derivation of an idealized Hubble's law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional Cartesian/Newtonian coordinate space, which, considered as a metric space, is entirely homogeneous and isotropic (properties do not vary with location or direction). Simply stated, the theorem is this:

"Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart."

In fact, this applies to non-Cartesian spaces as long as they are locally homogeneous and isotropic, specifically to the negatively and positively curved spaces frequently considered as cosmological models (see shape of the universe).

An observation stemming from this theorem is that seeing objects recede from us on Earth is not an indication that Earth is near to a center from which the expansion is occurring, but rather that observer in an expanding universe will see objects receding from them.

Ultimate fate and age of the universe

The value of the Hubble parameter changes over time, either increasing or decreasing depending on the value of the so-called deceleration parameter $q$, which is defined by

$$q = -\left(1+\frac{\dot H}{H^2}\right).$$

In a universe with a deceleration parameter equal to zero, it follows that $v = zc$, where $t$ is the time since the Big Bang. A non-zero, time-dependent value of $q$ simply requires integration of the Friedmann equations backwards from the present time to the time when the comoving horizon size was zero.

It was long thought that $q$ was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than $(1 + z)$ (which is about 14 billion years). For instance, a value for $q$ of 1/2 (once favoured by most theorists) would give the age of the universe as $H0$. The discovery in 1998 that $q$ is apparently negative means that the universe could actually be older than $q < -1$. However, estimates of the age of the universe are very close to $Ω_{M}$.

Olbers' paradox
The expansion of space summarized by the Big Bang interpretation of Hubble's law is relevant to the old conundrum known as Olbers' paradox: If the universe were infinite in size, static, and filled with a uniform distribution of stars, then every line of sight in the sky would end on a star, and the sky would be as bright as the surface of a star. However, the night sky is largely dark.

Since the 17th century, astronomers and other thinkers have proposed many possible ways to resolve this paradox, but the currently accepted resolution depends in part on the Big Bang theory, and in part on the Hubble expansion: in a universe that existed for a finite amount of time, only the light of a finite number of stars has had enough time to reach us, and the paradox is resolved. Additionally, in an expanding universe, distant objects recede from us, which causes the light emanated from them to be redshifted and diminished in brightness by the time we see it.

Dimensionless Hubble constant
Instead of working with Hubble's constant, a common practice is to introduce the dimensionless Hubble constant, usually denoted by $h$ and commonly referred to as "little h", then to write Hubble's constant $Ω_{Λ}$ as $h$ × 100 km⋅s−1⋅Mpc−1, all the relative uncertainty of the true value of $Ω_{M} > 1$ being then relegated to $h$. The dimensionless Hubble constant is often used when giving distances that are calculated from redshift $z$ using the formula $Ω_{Λ} = 0$. Since $Ω_{M} ≤ 1$ is not precisely known, the distance is expressed as:

$$cz/H_0\approx(2998\times z)\text{ Mpc }h^{-1}$$

In other words, one calculates 2998 × $z$ and one gives the units as Mpc $Ω_{Λ} = 0$ or $Ω_{Λ}$ Mpc.

Occasionally a reference value other than 100 may be chosen, in which case a subscript is presented after $h$ to avoid confusion; e.g. $H = 1/t$ denotes $1/H$ $km/s-1$, which implies $2/(3H)$.

This should not be confused with the dimensionless value of Hubble's constant, usually expressed in terms of Planck units, obtained by multiplying $1/H$ by $1.75$ (from definitions of parsec and $1/H$), for example for $H_{0}$, a Planck unit version of $1.2$ is obtained.

Acceleration of the expansion
A value for $q$ measured from standard candle observations of Type Ia supernovae, which was determined in 1998 to be negative, surprised many astronomers with the implication that the expansion of the universe is currently "accelerating" (although the Hubble factor is still decreasing with time, as mentioned above in the Interpretation section; see the articles on dark energy and the ΛCDM model).

Derivation of the Hubble parameter
Start with the Friedmann equation:

$$H^2 \equiv \left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\rho - \frac{kc^2}{a^2}+ \frac{\Lambda c^2}{3},$$

where $H$ is the Hubble parameter, $a$ is the scale factor, $G$ is the gravitational constant, $k$ is the normalised spatial curvature of the universe and equal to −1, 0, or 1, and $H_{0}$ is the cosmological constant.

Matter-dominated universe (with a cosmological constant)
If the universe is matter-dominated, then the mass density of the universe $ρ$ can be taken to include just matter so

$$\rho = \rho_m(a) = \frac{\rho_{m_{0}}}{a^3},$$

where $d ≈ c⁄H_{0} × z$ is the density of matter today. From the Friedmann equation and thermodynamic principles we know for non-relativistic particles that their mass density decreases proportional to the inverse volume of the universe, so the equation above must be true. We can also define (see density parameter for $H_{0}$)

$$\begin{align} \rho_c &= \frac{3 H_0^2}{8 \pi G}; \\ \Omega_m &\equiv \frac{\rho_{m_{0}}}{\rho_c} = \frac{8 \pi G}{3 H_0^2}\rho_{m_{0}}; \end{align}$$

therefore:

$$\rho=\frac{\rho_c \Omega_m}{a^3}.$$

Also, by definition, $$\begin{align} \Omega_k &\equiv \frac{-kc^2}{(a_0H_0)^2} \\ \Omega_{\Lambda} &\equiv \frac{\Lambda c^2}{3H_0^2}, \end{align}$$

where the subscript $h-1$ refers to the values today, and $h-1$. Substituting all of this into the Friedmann equation at the start of this section and replacing $a$ with $h70$ gives

$$H^2(z)= H_0^2 \left( \Omega_m (1+z)^{3} + \Omega_k (1+z)^{2} + \Omega_{\Lambda} \right).$$

Matter- and dark energy-dominated universe
If the universe is both matter-dominated and dark energy-dominated, then the above equation for the Hubble parameter will also be a function of the equation of state of dark energy. So now:

$$\rho = \rho_m (a)+\rho_{de}(a),$$

where $ρde$ is the mass density of the dark energy. By definition, an equation of state in cosmology is $H0 = 70 h70$, and if this is substituted into the fluid equation, which describes how the mass density of the universe evolves with time, then

$$\begin{align} \dot{\rho}+3\frac{\dot{a}}{a}\left(\rho+\frac{P}{c^2}\right)=0;\\ \frac{d\rho}{\rho}=-3\frac{da}{a}(1+w). \end{align}$$

If $w$ is constant, then

$$\ln{\rho}=-3(1+w)\ln{a};$$

implying:

$$\rho=a^{-3(1+w)}.$$

Therefore, for dark energy with a constant equation of state $w$, $\rho_{de}(a)= \rho_{de0}a^{-3(1+w)}$. If this is substituted into the Friedman equation in a similar way as before, but this time set $h70 = h / 0.7$, which assumes a spatially flat universe, then (see shape of the universe)

$$H^2(z)= H_0^2 \left( \Omega_m (1+z)^{3} + \Omega_{de}(1+z)^{3(1+w)} \right).$$

If the dark energy derives from a cosmological constant such as that introduced by Einstein, it can be shown that $H_{0}$. The equation then reduces to the last equation in the matter-dominated universe section, with $t_{P}$ set to zero. In that case the initial dark energy density $H0 = 70$ is given by

$$\begin{align} \rho_{de0} &= \frac{\Lambda c^2}{8 \pi G} \,, \\ \Omega_{de} &=\Omega_{\Lambda}. \end{align}$$

If dark energy does not have a constant equation-of-state $w$, then

$$\rho_{de}(a)= \rho_{de0}e^{-3\int\frac{da}{a}\left(1+w(a)\right)},$$

and to solve this, $Λ$ must be parametrized, for example if $ρm0$, giving

$$H^2(z)= H_0^2 \left( \Omega_m a^{-3} + \Omega_{de}a^{-3\left(1+w_0 +w_a \right)}e^{-3w_a(1-a)} \right).$$

Other ingredients have been formulated.

Hubble time
The Hubble constant $Ωm$ has units of inverse time; the Hubble time $tH$ is simply defined as the inverse of the Hubble constant, i.e.

$$t_H \equiv \frac{1}{H_0} = \frac{1}{67.8 \mathrm{~(km/s)/Mpc}} = 4.55\times 10^{17} \mathrm{~s} = 14.4 \text{ billion years}.$$

This is slightly different from the age of the universe, which is approximately 13.8 billion years. The Hubble time is the age it would have had if the expansion had been linear, and it is different from the real age of the universe because the expansion is not linear; it depends on the energy content of the universe (see ).

We currently appear to be approaching a period where the expansion of the universe is exponential due to the increasing dominance of vacuum energy. In this regime, the Hubble parameter is constant, and the universe grows by a factor $e$ each Hubble time:

$$H \equiv \frac{\dot a}{a} = \textrm{constant} \quad \Longrightarrow \quad a \propto e^{Ht} = e^{\frac{t}{t_H}}$$

Likewise, the generally accepted value of 2.27 Es−1 means that (at the current rate) the universe would grow by a factor of $e$$2.27$ in one exasecond.

Over long periods of time, the dynamics are complicated by general relativity, dark energy, inflation, etc., as explained above.

Hubble length
The Hubble length or Hubble distance is a unit of distance in cosmology, defined as $0$ — the speed of light multiplied by the Hubble time. It is equivalent to 4,420 million parsecs or 14.4 billion light years. (The numerical value of the Hubble length in light years is, by definition, equal to that of the Hubble time in years.) The Hubble distance would be the distance between the Earth and the galaxies which are receding from us at the speed of light, as can be seen by substituting $a0 = 1$ into the equation for Hubble's law, $a = 1/(1+z)$.

Hubble volume
The Hubble volume is sometimes defined as a volume of the universe with a comoving size of $P = wρc2$. The exact definition varies: it is sometimes defined as the volume of a sphere with radius $k = 0$, or alternatively, a cube of side $w = −1$. Some cosmologists even use the term Hubble volume to refer to the volume of the observable universe, although this has a radius approximately three times larger.

Determining the Hubble constant
The value of the Hubble constant, $Ωk$, tells the rate at which the universe is expanding. In 1929, Edwin Hubble determined for the first time this constant to be $500 km/s$ per million parsecs. Since then, Hubble constant has been actively measured using various methods. In the early days, Hubble, for example, used bright stars and the light of the "nebula" to estimate the redshift and determined the constant. Later, after type Ia supernova was found to be a better "standard candle" of distant galaxies, people used supernova to determining the redshift. These measurements need to determine the distance of the target stars or galaxies first. Uncertainties in the physical assumptions used to determine these distances have caused varying estimates of the Hubble constant.

More recently, scientists use CMB measurements (such as Planck's data) to determine the Hubble constant. The challenge of using this method is that its result varies depending on the cosmology models used. Due to the different values of Hubble constant estimated using different techniques, the determination of Hubble constant is an active research field (Hubble tension). The high accuracy measurement using James Webb Space Telescope in 2023 has confirmed the earlier observation of the Hubble Space Telescope, which gave a Hubble constant about $ρde0$ $74 km/s$.

Earlier measurement and discussion approaches
Hubble's original estimate of the constant now bearing his name, based on observations of Cepheid variable stars as "standard candles" to measure distance, was $500 km/s$ (much larger than the value astronomers currently calculate). Later observations by astronomer Walter Baade led him to realize that there were distinct "populations" for stars (Population I and Population II) in a galaxy. The same observations led him to discover that there are two types of Cepheid variable stars with different luminosities. Using this discovery, he recalculated Hubble constant and the size of the known universe, doubling the previous calculation made by Hubble in 1929. He announced this finding to considerable astonishment at the 1952 meeting of the International Astronomical Union in Rome.

For most of the second half of the 20th century, the value of $w(a)$ was estimated to be between $50 km/s$.

The value of the Hubble constant was the topic of a long and rather bitter controversy between Gérard de Vaucouleurs, who claimed the value was around 100, and Allan Sandage, who claimed the value was near 50. In one demonstration of vitriol shared between the parties, when Sandage and Gustav Andreas Tammann (Sandage's research colleague) formally acknowledged the shortcomings of confirming the systematic error of their method in 1975, Vaucouleurs responded "It is unfortunate that this sober warning was so soon forgotten and ignored by most astronomers and textbook writers". In 1996, a debate moderated by John Bahcall between Sidney van den Bergh and Gustav Tammann was held in similar fashion to the earlier Shapley–Curtis debate over these two competing values.

This previously wide variance in estimates was partially resolved with the introduction of the ΛCDM model of the universe in the late 1990s. Incorporating the ΛCDM model, observations of high-redshift clusters at X-ray and microwave wavelengths using the Sunyaev–Zel'dovich effect, measurements of anisotropies in the cosmic microwave background radiation, and optical surveys all gave a value of around 50–70 km/s/Mpc for the constant.

21st century measurements
More recent measurements from the Planck mission published in 2018 indicate a lower value of $67.66 km/s$, although, even more recently, in March 2019, a higher value of $74.03 km/s$ has been determined using an improved procedure involving the Hubble Space Telescope. The two measurements disagree at the 4.4σ level, beyond a plausible level of chance. The resolution to this disagreement is an ongoing area of active research.

In October 2018, scientists presented a new third way (two earlier methods, one based on redshifts and another on the cosmic distance ladder, gave results that do not agree), using information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), of determining the Hubble constant.

In July 2019, astronomers reported that a new method to determine the Hubble constant, and resolve the discrepancy of earlier methods, has been proposed based on the mergers of pairs of neutron stars, following the detection of the neutron star merger of GW170817, an event known as a dark siren. Their measurement of the Hubble constant is $73.3$ (km/s)/Mpc.

Also in July 2019, astronomers reported another new method, using data from the Hubble Space Telescope and based on distances to red giant stars calculated using the tip of the red-giant branch (TRGB) distance indicator. Their measurement of the Hubble constant is $69.8 km/s$.

In February 2020, the Megamaser Cosmology Project published independent results that confirmed the distance ladder results and differed from the early-universe results at a statistical significance level of 95%. In July 2020, measurements of the cosmic background radiation by the Atacama Cosmology Telescope predict that the Universe should be expanding more slowly than is currently observed.

In July 2023, an independent estimate of the Hubble constant was derived from the optical counterpart of a neutron-star merger, a so-called kilonova. Due to the blackbody nature of early kilonova spectra, such systems provide strongly constraining estimators of cosmic distance. Using the kilonova AT2017gfo, these measurements indicate a local-estimate of the Hubble constant of $67 km/s$.

Hubble tension
In the 21st century, multiple methods have been used to determine the Hubble constant. "Late universe" measurements using calibrated distance ladder techniques have converged on a value of approximately $73 km/s$. Since 2000, "early universe" techniques based on measurements of the cosmic microwave background have become available, and these agree on a value near $67 km/s$. (This is accounting for the change in the expansion rate since the early universe, so is comparable to the first number.) As techniques have improved, the estimated measurement uncertainties have shrunk, but the range of measured values has not, to the point that the disagreement is now highly statistically significant. This discrepancy is called the "Hubble tension".

The cause of the Hubble tension is unknown, and there are many possible proposed solutions. The most conservative is that there is an unknown systematic error affecting either early-universe or late-universe observations. Although intuitively appealing, this explanation requires multiple unrelated effects regardless of whether early-universe or late-universe observations are incorrect, and there are no obvious candidates. Furthermore, any such systematic error would need to affect multiple different instruments, since both the early-universe and late-universe observations come from several different telescopes.

Alternatively, it could be that the observations are correct, but some unaccounted-for effect is causing the discrepancy. If the cosmological principle fails (see "Violations of the cosmological principle" in the "Lambda-CDM model" article), then the existing interpretations of the Hubble constant and the Hubble tension have to be revised, which might resolve the Hubble tension. In particular, we would need to be located within a very large void, up to about a redshift of 0.5, for such an explanation to not be in tension with supernovae & baryon acoustic oscillation observations. Yet another possibility is that the uncertainties in the measurements could have been underestimated.

The most exciting possibility is new physics beyond the currently accepted cosmological model of the universe, the ΛCDM model. There are very many theories in this category, for example, replacing general relativity with a modified theory of gravity could potentially resolve the tension, as can a dark energy component in the early universe, dark energy with a time-varying equation of state, or dark matter that decays into dark radiation. A problem faced by all these theories is that both early-universe and late-universe measurements rely on multiple independent lines of physics, and it is difficult to modify any of those lines while preserving their successes elsewhere. The scale of the challenge can be seen from how some authors have argued that new early-universe physics alone is not sufficient; while other authors argue that new late-universe physics alone is also not sufficient. Nonetheless, astronomers are trying, with interest in the Hubble tension growing strongly in the past several years.

title: Hubble's law


text:
Talk:Hubble's law

Requested move 1 January 2023

 * 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: not moved. Numbers are moderately in favour of remaining in place (nb, two IP comments from very similar origin in Belgium were in support and counted as distinct). Support comments preferred to follow the IAU as authoritative, with expectation that WP:COMMONNAME would follow, while oppose comments held that the common name has not yet shifted, but may yet change in future. (non-admin closure) — HTGS (talk) 02:15, 9 January 2023 (UTC)

Hubble's law → Hubble–Lemaître law – This is now the new WP:COMMONNAME, after it was renamed in 2018. It is used by the relevant academic literature, see https://link.springer.com/chapter/10.1007/978-3-030-80654-5_5 for example. Sadly Google Ngram is not yet usable since it only works up to 2019. PhotographyEdits (talk) 17:26, 1 January 2023 (UTC)

 * See also previous discussion on this. Banedon (talk) 22:18, 1 January 2023 (UTC)
 * Same as previous. Lean yes since it's the IAU and it represents the consensus of most astronomers. Similarly when the IAU redefined Pluto as a dwarf planet in 2006 we didn't adopt a wait-and-see-if-it-becomes-common stance. However I don't feel strongly either way. It's just a name, and it's obvious what is being referred to regardless of whether it's called Hubble's law or Hubble-Lemaitre law. Banedon (talk) 12:44, 4 January 2023 (UTC)
 * Oppose. True common names are not determined by decree or by polls conducted only among specialist experts. — BarrelProof (talk) 04:48, 2 January 2023 (UTC)
 * Disagree: specialists have thought this through. Common names can still be used in the article (as is currently the case).
 * alex (talk) 13:05, 3 January 2023 (UTC)
 * Oppose. WP:COMMONNAME. The purpose of a name is to place a relatively-permanent label on an object, not to ascribe credit from moment to moment. Tarl N. ( discuss ) 12:16, 2 January 2023 (UTC)
 * Disagree: look at country names: they can change too. alex (talk) 13:06, 3 January 2023 (UTC)
 * Oppose. This is still the common name for the relation. It will take some years before we know whether the IAU recommendation becomes the name in common use. Their recommendations are not always followed, though it is good to recognize Lemaître. Common use means more than just academic papers, but textbooks and popular science articles. StarryGrandma (talk) 19:47, 2 January 2023 (UTC)
 * Disagree:
 * 1. Delaying the name change will make the common use more difficult, leading to a vicious circle.
 * 2. Fact is that the name change has been approved by a reference body.
 * alex (talk) alex (talk) 12:58, 3 January 2023 (UTC)
 * Support.
 * - This is now the correct name for this law, as decided by a reference organisation.
 * - It should be introduced as soon as possible to prevent memory to fade again.
 * - One should also take into account the risk of resistance to a name that could be seen as belonging to / originating from the English language region,
 * alex (talk) 13:03, 3 January 2023 (UTC)
 * Wikipedia does not make the news, and should only reflect what is going on in the real world. If not changing the article title causes the memory to fade again, then it was not the common name in the first place (or at the very least, can be shown to have not been a significant-enough part of history to merit changing the page name). In other words, we cannot make fetch happen. Primefac (talk) 13:43, 3 January 2023 (UTC) I also changed the indenting of your message mainly for formatting purposes.
 * One should also take into account the risk of resistance to a name that could be seen as belonging to / originating from the English language region I'm not sure what you mean by that. Could you please explain. Maybe you are trying to say that we should be careful because refusing to adopt the non-English name "Lemaître" could be seen as cultural bias on our part? That's the opposite of what you wrote, so I apologize, but hence why I ask for clarification. Renerpho (talk) 21:32, 5 January 2023 (UTC)
 * Or maybe you mean that the name "Hubble", which is an English name, may run into resistance from those who oppose the influence of English/American culture? I am guessing. Renerpho (talk) 21:35, 5 January 2023 (UTC)
 * Support It is now the official name by the IAU. 2A02:A03F:AA2C:7200:D01A:6015:8D63:34BB (talk) 13:40, 3 January 2023 (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.
 * Support. The International Astronomical Union is the internationally offically recognised body in charge of the nomenclature of everything in astronomy. And, although the International Astronomical Union cannot enforce the application of its resolutions, the fact that resolution B4 was adopted in October 2018, effectively means that the official name of the law is since then the "Hubble-Lemaître law".  (by Thierry Pauwels, member of the IAU)  — Preceding unsigned comment added by 2A02:A03F:F8CE:7300:F943:ECF2:918D:792A (talk) 15:42, 3 January 2023 (UTC)
 * The officialness of IAU's role is overstated, both on this talk page, and in general. They have no mandate to name physical laws. All they can do is make recommendations, which they call resolutions. People will follow those recommendations when they are convenient, and ignore them otherwise. That is a democratic process, but there are no actual votes involved. Scientists vote with what they publish in scientific journals, not with what they vote on at IAU meetings. The ongoing discussion about the term dwarf planet (used in the IAU sense by some astronomers, not used in the IAU sense by most planetary scientists, and no consensus on Wikipedia as of November 2022) is a good example, as is IAU's recommendation to stop using the unit erg (see my comments here). And even if IAU were the most official body in the world, that still would not matter. There is a policy WP:COMMONNAME on Wikipedia, and there is WP:OFFICIALNAME. Only one of those is a policy saying what the title of a Wikipedia page should be (hint, it's not WP:OFFICIALNAME). Renerpho (talk) 16:26, 5 January 2023 (UTC)
 * Oppose per WP:COMMONNAME. We use the most common English term for article titles, which is not necessarily the officially sanctioned term. Rreagan007 (talk) 19:49, 3 January 2023 (UTC)
 * Support. The IAU carries sufficient weight for its resolutions to be considered common use in encyclopedias and other reference works. In fact, IAU resolutions are challenged so rarely that the exceptions (see: status of Pluto) become newsworthy on their own.--Lieven Smits (talk) 11:00, 4 January 2023 (UTC)
 * Oppose per WP:COMMONNAME. -- Necrothesp (talk) 14:11, 4 January 2023 (UTC)
 * Support. If anyone gets to decide the names of astronomy-related things, it's the IAU. - Parejkoj (talk) 15:53, 4 January 2023 (UTC)
 * Comment What source are we using for determining the WP:COMMONNAME? I don't think it's fair to use sources from before the renaming, because that heavily skews it towards the old name. In newer academic sources, the longer name is being used. And it's not popular subject that newspapers and magazines write about, so purely using academic sources seems fine to me. PhotographyEdits (talk) 17:27, 4 January 2023 (UTC)
 * Oppose per WP:COMMONNAME. Nothing changed since Talk:Hubble's_law/Archive_3.   Headbomb {t · c · p · b} 17:42, 4 January 2023 (UTC)
 * Comment On another note, the WP:NAMECHANGES policy has not been mentioned yet, which says: "we give extra weight to independent, reliable English-language sources ("reliable sources") written after the name change. If the reliable sources written after the change is announced routinely use the new name, Wikipedia should follow suit and change relevant titles to match.". So that means my previous comment applies here. PhotographyEdits (talk) 18:24, 4 January 2023 (UTC)
 * Oppose. Considering Google Scholar results since 2019, I found 344 results for "Hubble's law", 1040 results for "Hubble law", and 239 results for "Hubble-Lemaître law" (dash/hyphen and diacritic don't matter for the numbers). While there are significant caveats in taking those numbers too seriously, I would generally conclude that, although Hubble–Lemaître has increased in popularity in the past few years, it has not (yet?) turned into the common name, even if we accept that WP:NAMECHANGES applies. Separately, I think the level of officialness of the 2018 recommendation is overstated; there's neither formal authority nor de facto precedent. From Nature news coverage: "The move seems to be the first time an organization has voted to alter the name of a scientific law — although some scientists doubt whether the change will be noticed. The IAU has been the arbiter of planet and moon names since 1919, and oversees astronomers’ official catalogue of star names, but it has no formal mandate over the names of scientific laws. Piero Benvenuti, a former IAU general secretary who proposed the motion, says that the new terminology is a recommendation only. 'If people will continue to use the Hubble law naming, nobody will object,' he says." (See also for other coverage of the 2018 vote.) Adumbrativus (talk) 06:46, 5 January 2023 (UTC)
 * Oppose, for now Nothing significant has changed since I voted oppose on this in November 2018, and what I said in the previous discussion still applies. IAU has given a recommendation, nothing more; they could not do more since they have no mandate to name physical laws. IAU has demonstrated in other instances that they often do not follow their own recommendations (see the ergs example I gave in the old discussion). While Hubble–Lemaître law has been used in a number of publications (20-30%, going by Adumbrativus's count above), that does not yet make it the common name. We are not here to set (or even to follow) trends, but to report on current knowledge. The common name may still change in the future, but we are not there yet. Renerpho (talk) 15:57, 5 January 2023 (UTC)

Hubble tension article
Would it be advisable to start a separate article on the Hubble tension? It has a lot of traction in science news and would be easier to follow the developments. A small section in this article does not seem enough. ReyHahn (talk) 11:20, 28 November 2023 (UTC)
 * I'd support a split, but someone who have to write the separate article. Banedon (talk) 00:44, 29 November 2023 (UTC)

Wirtz paragraph
@AThinkingScientist added the following paragraph and I want to explain why I am taking it out. As written, the paragraph disputes the title of the article: how can it be Hubble's law if Wirtz discovered it? The claim may be 100% accurate but we have no way to verify this claim. The paragraph now has primary references (which are nice to have) but as explained in WP:PRIMARY such references are not adequate for controversial content. If this claim is "notable", that is important enough to be included in the encyclopedia, then there should be secondary references to back up the claim. See also WP:PSTS. To put it another way, wikipedia editors don't do historical analysis, we summarize historical analysis.
 * Before Hubble, German astronomer Carl Wilhelm Wirtz had, in two publications dating 1922 and 1924, already deduced with his own data that galaxies that appeared smaller and dimmer had larger redshifts and thus that more distant galaxies recede faster from the observer.

An addition issue is including the content directly in the lead is not correct. The content needs to be in the body of the article. Johnjbarton (talk) 15:47, 7 July 2024 (UTC)
 * "In Wikipedia, the lead section is an introduction to an article and a summary of its most important contents."

 * Thank you Johnbarton. This can be placed into the body. It is true that the discovery of the expanding Universe was achieved by Wirtz, at a time when astronomers had not realised this to be possible. It is correct to document this properly. Hubble did not discover the expansion, although he contributed significantly to constrain it with improved data. Given the political turmoils of that time, the German contribution was "forgotten".
 * A secondary reference is by Prof. Dr. Immo Appenzeller, Sterne und Weltraum, November 2009, pages 44-52 ("Carl Wirtz und die Hubble Beziehung"), wherein the history and contribution by Wirtz are accounted for. Would this be acceptable as a secondary reference? Not many people have followed this up, precisely because this collides with the generally-held view that Hubble discovered the expansion.
 * (I am not German by the way and am merely aiming to have a correct historical record of this affair on Wikipedia.) AThinkingScientist (talk) 16:25, 7 July 2024 (UTC)
 * I tried to place this under "Slipher's observations with the secondary reference to Prof. Appenzeller's article.

 * But it gives an error message I cannot solve. It would be welcome if someone can help to import this properly. Wikipedia has a page on Sterne und Weltraum. AThinkingScientist (talk) 16:52, 7 July 2024 (UTC)
 * I think we need to do some more research. See This suggests the story is more complicated. Johnjbarton (talk) 17:25, 7 July 2024 (UTC)
 * Some more refs:
 * GLASS, I.S., 'EDWIN HUBBLE: JOURNEYING TO THE EDGE', Revolutionaries of the Cosmos: The Astro-Physicists (Oxford, 2008; online edn, Oxford Academic, 1 Jan. 2010), https://doi-org.wikipedialibrary.idm.oclc.org/10.1093/acprof:oso/9780199550258.003.0009,
 * "Duerbeck and Seitter (2000) cynically remark that ‘Hubble was the last of the early cosmologists who believed that his result confirmed the de Sitter model’. While this is superficially true, Hubble's work was by far the most systematic, especially as to finding distances, so he was not just the last person to point out the result, but he had said the last word on the matter. Other investigators, such as de Sitter himself, Wirtz, Lundmark and Silberstein had been hinting that the high velocities of the galaxies were of cosmological origin. Hetherington (1986) suggests that Hubble's pre-eminence was a result of his legal training that made him adept at advocating his point of view in a highly convincing manner."
 * "Modern Cosmology in Retrospect",  ISBN:9780521372138 United Kingdom, Cambridge University Press, 1990. contains a chapter by Seitter and Duerbeck devoted to Wirtz's work.  Also discusses Lundmark and others.
 * Kragh, H. (2014, November). Historical aspects of post-1850 cosmology. In AIP Conference Proceedings (Vol. 1632, No. 1, pp. 3-26). American Institute of Physics.
 * "With more and better data than previous workers in the field, Hubble showed that up to a distance of two megaparsecs (corresponding to a recessional velocity v ≅ 1,000 km/s) the redshifts or Doppler-velocities varied roughly linearly with the distances. In other words, he established as an empirical law that v = Hr, with H soon to be known as the Hubble constant."
 * "It is important to recognize that he did not interpret the redshifts or “apparent velocities” as Doppler shifts caused by the galaxies actually receding from the observer. Nor did he suggest that space is expanding, such as Lemaître had done. As he emphasized in a letter to de Sitter of 1931, he was content having demonstrated an empirical correlation."
 * Johnjbarton (talk) 16:37, 8 July 2024 (UTC)

Reference thoughts
With >150 references, most of them being journal articles and most of those being dozen-author articles, I was thinking it might be best for readability of the code to go with a list-defined reference as seen in places like List of largest stars and other journal-heavy articles. However, I know this can be potentially controversial so I thought I would bring it up before I spend the time to do so unilaterally. Primefac (talk) 18:52, 7 July 2024 (UTC)

 * Sorry I don't follow your suggestion. How about splitting the long list out and only having a summary here. Johnjbarton (talk) 21:44, 7 July 2024 (UTC)
 * Johnjbarton, see . Instead of having each reference clogging up the body of the text, they're listed at the bottom as named references to make reading the wikitext a bit easier. Primefac (talk) 22:26, 7 July 2024 (UTC)
 * It seems like this can be done selectively? If yes, it is a clear win if the clog bothers you. Johnjbarton (talk) 22:52, 7 July 2024 (UTC)

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

title: Talk:Hubble's law


text:
Mercedes-Benz Group

The Mercedes-Benz Group AG (previously named Daimler-Benz, DaimlerChrysler and Daimler) is a German multinational automotive corporation headquartered in Stuttgart, Baden-Württemberg, Germany. It is one of the world's leading car manufacturers. Daimler-Benz was formed with the merger of Benz & Cie., the world's oldest car company, and Daimler Motoren Gesellschaft in 1926. The company was renamed DaimlerChrysler upon the acquisition of American automobile manufacturer Chrysler Corporation in 1998, and was again renamed Daimler AG upon divestment of Chrysler in 2007. In 2021, Daimler AG was the second-largest German automaker and the sixth-largest worldwide by production. In February 2022, Daimler was renamed Mercedes-Benz Group as part of a transaction that spun-off its commercial vehicle segment as an independent company, Daimler Truck.

The Mercedes-Benz Group's marques are Mercedes-Benz for cars and vans (including Mercedes-AMG and Mercedes-Maybach) and Smart. It has shares in other vehicle manufacturers such as Daimler Truck, Denza, BAIC Motor and Aston Martin.

By unit sales, the Mercedes-Benz Group is the tenth-largest car manufacturer in the world; shipping two million passenger vehicles in 2021 and by revenue the sixth-largest car manufacturer worldwide in 2022. In 2023, the company was ranked 42nd in the Forbes Global 2000. The group provides financial services through its Mercedes-Benz Mobility arm. The company is a component of the Euro Stoxx 50 stock market index. The central company headquarters, the Mercedes-Benz offices, a car assembly plant, the Mercedes-Benz Museum and the Mercedes-Benz Arena are situated in the Mercedes-Benz complex in Stuttgart.

1926–1998: Daimler-Benz
The Mercedes-Benz Group origin is in an Agreement of Mutual Interest signed on 1 May 1924 between Benz & Cie. (founded in 1883 by Carl Benz) and Daimler Motoren Gesellschaft (founded in 1890 by Gottlieb Daimler and Wilhelm Maybach). Both companies continued to manufacture their separate automobile and internal combustion engine marques until 28 June 1926, when Benz & Cie. and Daimler-Motoren-Gesellschaft formally merged – becoming Daimler-Benz AG (Aktiengesellschaft) – and agreed that thereafter, all of the factories would use the brand name of "Mercedes-Benz" on their automobiles. The inclusion of the name Mercedes in the new brand name honored the most important model series of DMG automobiles, the Mercedes series, which were designed and built by Wilhelm Maybach. They derived their name from a 1900 engine named after the daughter of Emil Jellinek. Jellinek became one of DMG's directors in 1900, ordered a small number of motor racing cars built to his specifications by Maybach, stipulated that the engine must be named Daimler-Mercedes, and made the new automobile famous through motorsports. That race car later became known as the Mercedes 35 hp. The first of the series of production models bearing the name Mercedes had been produced by DMG in 1902. Jellinek left the DMG board of directors in 1909.

The name of Daimler as a marque of automobiles had been given by Gottlieb Daimler for use by other companies. It is or was used principally by Daimler Motor Company and Austro-Daimler later Steyr-Daimler-Puch but also, very briefly by Daimler Manufacturing Company and Panhard-Daimler, and others. The new company, Daimler-Benz, did not obtain consent to include Daimler in its brand name and used the name Mercedes to represent the Daimler-Motoren-Gesellschaft interest. Karl Benz remained as a member of the board of directors of Daimler-Benz AG until his death in 1929.

Although Daimler-Benz is best known for its Mercedes-Benz automobile brand, during World War II, it also created a notable series of engines for German aircraft, tanks, and submarines. Its cars became the first choice of many Nazi, Fascist Italian, and Japanese officials including Hermann Göring, Adolf Hitler, Benito Mussolini and Hirohito, who most notably used the Mercedes-Benz 770 luxury car. Daimler also produced parts for German arms, most notably barrels for Mauser Kar98k rifles. During World War II, Daimler-Benz had over 60,000 concentration camp prisoners and other forced laborers to build machinery. After the war, Daimler admitted to its links and coordination with the Nazi government.

In 1966, Maybach-Motorenbau GmbH merged with Mercedes-Benz Motorenbau Friedrichshafen GmbH to form Maybach Mercedes-Benz Motorenbau GmbH, under partial ownership by Daimler-Benz. The company is renamed Motoren und Turbinen-Union Friedrichshafen GmbH (MTU Friedrichshafen) in 1969.

In 1989, Daimler-Benz InterServices AG (Debis) was created to handle data processing, financial and insurance services, and real estate management for the Daimler group.

In 1995, MTU Friedrichshafen became a wholly owned subsidiary of Daimler-Benz.

1998–2007: DaimlerChrysler
In a so-called "merger of equals," or "marriage made in heaven", according to its then CEO and architect Jürgen E. Schrempp, Daimler-Benz and United States-based automobile manufacturer Chrysler Corporation, the smallest of the main three American automakers, merged in 1998 in an exchange of shares and formed DaimlerChrysler AG. Valued at US$38 billion, it was the world's largest ever cross-border deal.

The terms of the merger allowed Daimler-Benz's non-automotive businesses such as Daimler-Benz InterServices AG, "debis AG" for short, to continue to pursue their respective strategies of expansion. debis AG reported revenues of $8.6 bn (DM 15.5 bn) in 1997.

The merger was contentious with investors launching lawsuits over whether the transaction was the 'merger of equals' that senior management claimed or actually amounted to a Daimler-Benz takeover of Chrysler. A class action investor lawsuit was settled in August 2003 for US$300 million while a suit by billionaire investor activist Kirk Kerkorian was dismissed on 7 April 2005. The transaction claimed the job of its architect, Chairman Jürgen E. Schrempp, who resigned at the end of 2005 in response to the fall of the company's share price following the transaction.

Another issue of contention is whether the merger delivered promised synergies and successfully integrated the two businesses. Martin H. Wiggers' concept of a platform strategy, like the VW Group's, was implemented only for a few models, so the synergy effects in development and production were low. As late as 2002, DaimlerChrysler appeared to run two independent product lines. Later that year, the company launched products that did integrate elements from both sides of the company, including the Chrysler Crossfire, which was based on the Mercedes SLK platform and utilized Mercedes's 3.2 L V6, and the Dodge Sprinter/Freightliner Sprinter, a re-badged Mercedes-Benz Sprinter van.

In 2000, DaimlerChrysler acquired the Detroit Diesel Corporation and placed its on-highway division under Daimler Trucks North America. The off-highway division was placed under MTU Friedrichshafen to form MTU America. Detroit Diesel branding has been maintained by DTNA and MTU America. In 2005, MTU-Friedrichshafen was sold to the Swedish investment firm EQT Partners. That same year, DaimlerChrysler entered into an alliance with Mitsubishi Motors Corporation in an effort to reach the Asian market. The alliance resulted in the platform sharing between the 2002-2013 Colt and first-generation Smart Forfour, but the declining performance of Mitsubishi led DaimlerChrysler to sell its shares back by 2004.

In 2006, Chrysler reported losses of US$1.5 billion. It then announced plans to lay off 13,000 employees in mid-February 2007, close a major assembly plant and reduce production at other plants in order to restore profitability by 2008. That same year, Chrysler was overtaken by Toyota in the US market, leaving it outside of the traditional "Big Three" of US automakers for the first time.

DaimlerChrysler had reportedly approached other carmakers and investment groups to sell Chrysler in early 2007. General Motors was reported to be a suitor, but Daimler agreed to sell the Chrysler unit to Cerberus Capital Management in May 2007 for US$6 billion and completed the sale on 3 August 2007. The original agreement stated that Cerberus would take an 80.1 percent stake in the new company, Chrysler Holding LLC. DaimlerChrysler changed its name to Daimler AG and retained the remaining 19.9% stake in the separated Chrysler LLC.

The terms saw Daimler pay Cerberus US$650 million to take Chrysler and associated liabilities off its hands. Of the US$7.4 billion purchase price, Cerberus Capital Management was to invest US$5 billion in Chrysler Holdings and US$1.05 billion in Chrysler's financial unit. The de-merged Daimler AG received US$1.35 billion directly from Cerberus but directly invested US$2 billion in Chrysler itself. Chrysler filed bankruptcy in 2009.

DC Aviation rose in 2007 from the previous DaimlerChrysler Aviation, an auxiliary of DaimlerChrysler AG, which was established in 1998.

2007–2022: Daimler AG
In May 2010, the Shenzhen BYD Daimler New Technology Co., Ltd., trading as "Denza" was established between BYD and Daimler to produce luxury electric vehicles.

In November 2014, Daimler announced it would acquire 25 percent of Italian motorcycle producer MV Agusta for an undisclosed fee. MV Holding acquired the 25 percent of MV Agusta back from Daimler in December 2017.

On 3 August 2015, Nokia announced that it had reached a deal to sell its Here digital maps division to a consortium of three German automakers—BMW, Daimler AG, and Volkswagen Group, for €2.8 billion. This was seen as an indication that the automakers were interested in automated cars.

In 2017, Daimler announced a series of acquisitions and partnerships with car startups focused on car sharing, in a move towards what it sees as the next generation of car ownership and usage. Part of its corporate strategy is to "transition from being an automobile manufacturer to a mobility services provider".

In April 2017 it announced a partnership with Via, a New York-based ride-sharing app, to launch a new ride-sharing service across Europe. In September, it was announced that Daimler had led a fundraising round for car-sharing start up Turo, which is a platform that lets owners rent their vehicles out to other users. It also acquired Flinc, a German startup that has built an app for peer-to-peer-style carpooling, has invested in Storedot, Careem, Blacklane and FlixBus, and has acquired car2go and mytaxi (now Free Now).

Li Shufu of Chinese automobile manufacturer Geely took a 9.69% stake in the company, through Tenaciou3 Prospect Investment Limited, in February 2018, making it the company's largest single shareholder. Geely is already known from its ownership of Volvo Car Corporation. In September 2018, Daimler invested $155 million in US-based electric bus and its battery management technology manufacturer Proterra.

In July 2019, BAIC Group purchased a 5% stake in Daimler, which is a reciprocal shareholder in BAIC's Hong Kong listed subsidiary.

In September 2019, Daimler announced that it would be "stopping its internal combustion engine development initiatives as part of its efforts to embrace electric vehicles."

In February 2020, Daimler partnered with Twelve to create the world's first C-pillar made with polycarbonate from CO2 electrolysis in an effort towards a fully carbon neutral fleet.

In September 2020, the company was fined 875 million dollars by the United States for having violated the Clean Air Act. It agreed to pay $1.5 billion to settle all related court actions.

In February 2021, Daimler said it planned to rename itself adopting the name of its flagship marque, Mercedes-Benz, and spun off its heavy commercial vehicles unit, Daimler Truck, into a separate listed company. Daimler Truck is listed on the Frankfurt Stock Exchange and its first trading day was on 10 December 2021.

In the 2021 review of WIPO's annual World Intellectual Property Indicators Daimler ranked 8th in the world, with 65 of its designs in industrial design registrations being published under the Hague System during 2020. This position is up on its previous 10th-place ranking in 2019.

2022–present: Mercedes-Benz Group
On 28 January 2022, CEO Ola Källenius announced that Daimler will be rebranded as Mercedes-Benz to pursue a higher valuation for the company as it shifts deeper into high-tech electric vehicles. On 1 February 2022, Daimler officially changed its registered company name to Mercedes-Benz Group AG.

Sales of Mercedes-Benz Group vehicles in 2023 - 2,491,600 (+1.5%). Sales of superior products increased: Mercedes-Maybach (+19%), G-Class (+11%) and Mercedes-AMG (+4%). Fully electric Mercedes-Benz passenger car sales rose by 73% during the year. Only Core segment sales declined by 2%, with 1,096,800 units sold due to supplier bottlenecks and the transition to the new E-Class.

Management
Ola Källenius became the Chairman of Mercedes-Benz Group and Head of Mercedes-Benz Cars on 22 May 2019. , the members of the Board of Management of Mercedes-Benz Group AG were:
 * Ola Källenius: Chairman of the Board of Management of Mercedes-Benz Group AG and Mercedes-Benz AG.
 * Renata Jungo Brüngger: Integrity and Legal Affairs.
 * Jörg Burzer: Production and Supply Chain Management.
 * Sabine Kohleisen: Human Resources and Director of Labor Relations.
 * Markus Schäfer: Chief Technology Officer responsible for Development and Purchasing.
 * Britta Seeger: Mercedes-Benz Cars Marketing and Sales.
 * Hubertus Troska: Greater China
 * Harald Wilhelm: Finance and Controlling and Head of Mercedes-Benz Mobility

2019 shareholder structure according to the BaFin
According to the German Securities Trading Act (Wertpapierhandelsgesetz, WpHG) paragraph § 38 owner of rights like financial options to buy common shares with voting rights have to be reported in case certain threshold values are achieved. These owners must report the sum of owned common shares and potential rights to buy additional shares.

The German Federal Financial Supervisory Authority (BaFin) reports the following shareholder structure based on § 39 WpHG, (Date: Tuesday, 19 November 2019):

 * Bank of America Corporation: 20.25%
 * BlackRock, Inc.: 5.09%
 * Harris Associates L.P.: 4.93%
 * Li Shufu with Tenaciou3 Prospect Investment Limited: 9.69%
 * Morgan Stanley: 5.7%
 * People's Republic of China: 5%

EADS shareholding
As of March 2010, Daimler owned a 22.5% share of EADS.

In April 2013, Daimler sold its shares in EADS, and the same year, EADS restructured itself into a new aerospace company named Airbus.

Daimler-Benz AG (1926–1998)

 * Wilhelm Kissel (1926–1942)
 * Wilhelm Haspel (1942–1952)
 * Heinrich C. Wagner (1952)
 * Fritz Koenecke (1952–1960)
 * Walter Hitzinger (1961–1966)
 * Joachim Zahn (1966–1979)
 * Gerhard Prinz (1980–1983)
 * Werner Breitschwerdt (1983–1987)
 * Edzard Reuter (1987–1995)
 * Jürgen E. Schrempp (1995–1998)

DaimlerChrysler AG (1998–2007)

 * Jürgen E. Schrempp (1998–2006)
 * Robert James Eaton (co-CEO, 1998–2000)
 * Dieter Zetsche (2006–2007)

Daimler AG (2007–2022)

 * Dieter Zetsche (2007–2019)
 * Ola Källenius (2019–2022)

Mercedes-Benz Group AG (2022–present)

 * Ola Källenius (2022–present)

Business trends
The key trends for the Mercedes-Benz Group are (as at the financial year ending 31 December):

North Charleston expansion
On 5 March 2015, Daimler AG announced a 1,200-job package to the North Charleston region for its van plant, to allow the company to start manufacturing Mercedes-Benz Sprinter vans from scratch to meet demand in North America. From 2010, these vans were set up in Germany, then shipped to the United States partially disassembled for reassembly to avoid import tariffs. A Daimler official said that the Sprinter's popularity in North America was making that process less efficient. The North Charleston plant had been employing only 100 workers. The Sprinter is available on the U.S. market as a panel van, crew bus and chassis in several variants with three lengths and roof heights, six-cylinder diesel or gasoline engines. The Sprinter has been assembled and sold in the United States since 2001.

Brands
The Mercedes-Benz Group sells automobiles under the following brands worldwide:
 * Mercedes-Benz Cars
 * Mercedes-Benz
 * Mercedes-AMG – High performance vehicles
 * Mercedes-Maybach – Introduced November 2014
 * Smart
 * Maybach – production ended in 2012, but the ultra-high end S-class and GLS-class is sold as Mercedes-Maybach
 * Mercedes-Benz Vans
 * Mercedes-Benz (vans group)
 * Mercedes-Benz Mobility
 * Mercedes-Benz Bank
 * Mercedes-Benz Financial Services
 * Others
 * Mercedes AMG High Performance Powertrains (builds engines for Formula One racing)

Former
Share Now - Now part of Stellantis

Locations
The Mercedes-Benz Group has a worldwide network of production plants and research centers. The following list describes all locations around the world.

Holdings
In 2015, Daimler held interests in the following companies:
 * 89.29% Mitsubishi Fuso Truck and Bus Corporation of Japan
 * 50% Denza (Shenzhen BYD Daimler New Technology Co., Ltd)
 * 12% Beijing Automotive Group (BAIC)
 * 15% KAMAZ of Russia
 * 20% Aston Martin Lagonda

Until the end of 2011, the company had also held shares in McLaren Group. Daimler held 25% of MV Agusta of Italy until 2017. Daimler sold its 50% stake in Engine Holding, to its joint venture partner, Rolls-Royce Holdings in 2014. It is now called Rolls-Royce Power Systems AG. Daimler used to own 50.1% Automotive Fuel Cell Cooperation of Canada but the joint venture was closed in 2018.

FAW and later Beijing Automotive Group
From 1986 to 1989, Daimler produced the Mercedes-Benz W123 (200 and 230E) sedans in China under a joint venture with FAW Group, with 828 units assembled in Changchun.

Beijing Jeep was a joint venture between Chrysler and BAIC Motor. After DaimlerChrysler was formed, its legal name was changed to Beijing Benz in 2004, and it started producing Mercedes-Benz models in 2006. The partnership has continued during the Daimler AG era.

In February 2013, Daimler acquired a 12% stake in BAIC Motor, becoming the first western car manufacturer to own a stake in a Chinese company.

Daimler works with China's Beiqi Foton (a subsidiary of BAIC) to build Auman trucks.

Force Motors
Daimler has partnered with Force Motors since the 1950s, they let Force Motors use the OM616 on the Force Gurkha and Trax.

Denza
In 2010 BYD Auto and Daimler AG created a new joint venture Shenzhen BYD Daimler New Technology Co., Ltd. In 2012 the new brand Denza was launched by the joint venture to specialise in electric cars.

Fujian Benz
In 2007 Daimler created a joint venture with Fujian Motors Group and China Motor Corporation and created Fujian Benz (originally Fujian Daimler Automotive Co.).

SsangYong Motors
Between 1990 and 2010 SsangYong partnered with Daimler-Benz. The deal was for SsangYong to develop an SUV with Mercedes-Benz technology. This was supposedly to allow SsangYong to gain footholds in new markets without having to build their own infrastructure (utilizing existing Mercedes-Benz networks) while giving Mercedes a competitor in the then-booming SUV market. This resulted in the Musso, which was sold first by Mercedes-Benz and later by SsangYong. SsangYong further benefited from this alliance, long after Daimler-Benz stopped selling the Musso, producing a badge engineered version of the Mercedes-Benz MB100, the Istana and using Daimler designs in many other models, including the second-generation Korando (engine and transmission), the Rexton (transmission), the Chairman H (chassis and transmission) and the Kyron (transmission). Ssangyong Also Partnered with Daewoo Motors to sell the chairman, Korando, Istana, and Musso to the rest of South Korea and Asia, Ssangyong later partnered with SAIC (Roewe) to rebadge the Chairman W in china as the Roewe R95/850 and the Kyron as Roewe W5 and also use the Mercedes-Benz 5G-Tronic transmission for the W5, SAIC has been working with Daimler since the 1964 with the Shanghai SH760 using a modified W121 chassis. Micro another company that rebadged Ssangyong's like Kyron, Actyon and Rexton using Mercedes-Benz engines.

Renault-Nissan-Mitsubishi and Daimler Alliance
On 7 April 2010, Renault-Nissan executives, Carlos Ghosn and Dieter Zetsche announced a partnership between the three companies. The first fruits of the alliance in 2012 included engine sharing (Infiniti Q50 utilising Mercedes diesel engines) and a re-badged Renault Kangoo being sold as a Mercedes-Benz Citan.

Electric
Daimler AG and the utility company RWE AG were set in 2009 to begin a joint electric car and charging station test project in the German capital, Berlin, called "E-Mobility Berlin".

Following trials in 2007 and then with Tesla in 2009, Daimler is building a production Smart electric drive car using Tesla's battery technology. Daimler temporarily invested in Tesla, saving it from bankruptcy. Daimler's joint venture with BYD has resulted in the creation of the new brand Denza.

In 2016, Daimler subsidiary ACCUMOTIVE announced their stationary batteries, to store up to 20 kWh of solar power for later use. Daimler plans to invest €1.5 billion in battery technology, and unveiled a factory in Kamenz in May 2017.

In September 2019, Daimler redirected its internal combustion engine development initiatives to focus on electric vehicle technologies, leaving electric propulsion rather less of an "alternative" and more the Daimler mainline. Their Research and Development department has developed a compostable battery that uses graphene-based organic cell chemistry. This means that no rare, toxic metals are needed for the battery, which makes it 100% recyclable.

As of 2023, Mercedes-Benz has released fully electric cars.

Fuel cell
Daimler has been involved with fuel cell vehicle development for some time, with a number of research and concept vehicles shown and demonstrated, the first being the 2002 Mercedes-Benz F-Cell car and the Mercedes-Benz Citaro hydrogen bus. In 2013, the Renault-Nissan/Daimler alliance was joined by Ford to further develop the fuel cell technology with an aim for production by 2017.

Hybrid
Mercedes-Benz launched its first passenger car model equipped with a hybrid drive system in summer 2009, the Mercedes-Benz S-Class 400 Hybrid. and the Citaro Hybrid bus in 2007. Daimler Trucks and Mitusbishi Fuso have also trialed various hybrid models including the Mitsubishi Fuso Canter Eco Hybrid and Mitsubishi Fuso Aero Star Aero Star Eco Hybrid bus.

Biofuel research
Daimler AG is involved in a joint project with Archer Daniels Midland Company and Bayer CropScience to develop the semi-evergreen shrub jatropha curcas as a biofuel.

Formula One
On 16 November 2009, Daimler and Aabar Investments purchased a 75.1% stake in Brawn GP (Daimler holding 45.1%). The company was rebranded as Mercedes GP with its base in Brackley, UK and Ross Brawn remaining team principal. The Brawn purchase led to Daimler selling back its stake in McLaren in stages, completed in 2011. Mercedes continued to provide sponsorship and engines to McLaren until 2014.

Prior to the 2011 season, Daimler and Aabar Investments purchased the remaining 24.9% stake owned by the team management in February 2011. In November 2012 Aabar Investments sold its remaining shares, leaving the team (rebranded as Mercedes AMG Petronas F1 Team) wholly Daimler-owned.

Daimler also owns Mercedes AMG High Performance Powertrains which, as of 2021, supplied engines to Aston Martin, Williams and McLaren, in addition to Mercedes AMG Petronas.

O-Bahn
The O-Bahn system was conceived by Daimler-Benz to enable buses to avoid traffic congestion by sharing tram tunnels in the German city of Essen. However, the project did not materialise there; the project was built in the Australian city of Adelaide.

Bribery and corruption
On 1 April 2010, Daimler AG's German and Russian subsidiaries each pleaded guilty to two counts of bribery charges brought by the U.S. Justice Department and the U.S. Securities and Exchange Commission. The parent company made a US$185 million settlement, but the company and its Chinese subsidiary remained subject to a two-year deferred prosecution agreement requiring further cooperation with regulators, adherence to internal controls and meeting other terms before final sentencing. Daimler would face harsher penalties should it fail to meet the terms of the agreement during the two-year period.

Additionally, Louis J. Freeh, a former director of the Federal Bureau of Investigation, served as an independent monitor to oversee Daimler's compliance with anti-bribery laws.

U.S. prosecutors accused key executives of Daimler, Daimler subsidiaries, and Daimler affiliates of illegally showering foreign officials with money and gifts between 1998 and 2008 to secure government contracts around the world. The investigation for the case revealed that Daimler improperly paid some $56 million in bribes related to more than 200 transactions in at least 22 countries (including China, Russia, Turkey, Hungary, Greece, Latvia, Serbia and Montenegro, Egypt, and Nigeria, among other places) that, in return, awarded the company $1.9 billion in revenue and at least $91.4 million in illegal profits.

The SEC case was sparked in 2004 after David Bazzetta, a former auditor at then DaimlerChrysler Corp, filed a whistleblower complaint after he was fired for raising questions about bank accounts controlled by Mercedes-Benz units in South America. Bazzetta alleged that he learned in a July 2001 corporate audit executive committee meeting in Stuttgart that business units "continued to maintain secret bank accounts to bribe foreign government officials", though the company knew the practice violated U.S. laws.

In another attempt to silence Bazzetta, Daimler later offered to settle his termination of employment suit out of court and he eventually accepted a settlement. But Daimler's strategy with Bazzetta proved to be a failure as the U.S. criminal investigation for violating anti-bribery laws was already underway in what has been one of the most wide-ranging cases brought against a foreign corporation.

According to the charges, the bribes were frequently made by over-invoicing customers and paying the excess back to top government officials or their proxies. The bribes also took the form of luxury European vacations, armored Mercedes vehicles for high-ranking government officials and a birthday gift to the dictator of Turkmenistan, Turkmenbashi (Saparmurat Niyazov), including a golden box and 10,000 copies of his personal manifesto, Ruhnama, translated into German.

Investigators also found that the firm violated the terms of the United Nations' Oil-for-Food Programme with Iraq by giving kickbacks worth 10% of the contract values to officials within the Iraqi government, then led by Saddam Hussein. The SEC said the company made more than $4 million in profit from the sale of vehicles and spare parts in the corrupt oil-for-food deals.

U.S. prosecutors further alleged that some bribes were paid through shell companies based in the U.S. "In some cases Daimler wired these improper payments to U.S. bank accounts or to the foreign bank accounts of U.S. shell companies in order to transmit the bribe", the court papers said.

Prosecutors said that Daimler engaged in a "long-standing practice" of paying bribes, due in part to a corporate culture that encouraged the practice.

"Using offshore bank accounts, third-party agents and deceptive pricing practices, [Daimler AG, its subsidiaries and its affiliates] saw foreign bribery as a way of doing business," said Mythili Raman, a principal deputy in the Justice Department's criminal division.

"It is no exaggeration to describe corruption and bribe-paying at Daimler as a standard business practice", Robert Khuzami, director of the SEC's enforcement division, said in a statement.

As per the agreement with prosecutors, the two Daimler subsidiaries admitted to knowingly violating the Foreign Corrupt Practices Act, which bars companies and their officials from paying bribes to foreign officials to win business. The Foreign Corrupt Practices Act applies to any company that lists its shares on U.S. stock exchanges. Daimler AG was listed with the symbol "DAI" on the New York Stock Exchange, giving the Justice Department jurisdiction over the German car maker's payments in countries around the globe. Judge Richard J. Leon of the United States District Court in Washington, D.C., approved the plea agreement and settlement, calling it a "just resolution". Daimler AG agreed to settle for $2.2 billion to US and California state regulators.

title: Mercedes-Benz Group