Bruno Dupeyron

Secluding North America's labour migrants: Notes on the International Organization for Migration's compassionate mercenary business 1

Movements of People (NIROMP), funded by the Swedish, Dutch and Swiss governments (Ghosh 2000). Ghosh proposed a comprehensive international migration regime, designed to tackle what was perceived as current and future migration policy crises, and focuses on both migrants and refugees (Geiger and Pécoud 2010). Yet, Sassen argues that these two categories, migrants and refugees, cannot be merged: "there are separate regimes for refugees in all these countries and an international regime as well, something that can hardly be said for immigration " (1996, 64).

Nonetheless, Ghosh's 'migration management' approach was welcomed and later borrowed by the International Organization for Migration (IOM). This notion of 'migration management' became a mantra of the IOM, "committed to the principle that humane and orderly migration benefits migrants and society" (IOM 2015e).

The IOM is an intergovernmental organization (IGO), created in 1951 as an operational organization (as opposed to a full-fledged migration organization now), known as the Provisional Intergovernmental Committee for the Movement of Migrants from Europe (PICMME). The context of the origins of the PICMME deserves to be examined briefly. After the Second World War, approximately 11 million displaced people brought about serious socio-economic concerns for European governments. The problem was generally framed as an economic issue of surplus populations in Europe, surplus populations that required resettlement to certain countries with manpower needs, e.g., the United States (US), Canada, Australia, and so on. Yet, there was no consensus over an appropriate solution, as the United States disagreed with multilateral international organizations, e.g., the United Nations (UN). In the midst of the cold war, the United States insisted on limiting international interferences over migrant and refugee policy issues, and thus proposed to create a basic institution with specific functions, based on an intergovernmental structure driven by nation-states' economic agenda. Conversely, the UN supported the idea of an

Introduction

The re(b)ordering efforts made by states over the last three decades, for instance the securitization of some border areas and harsher visa policies, may denote an evolution of the international migration regime. The increase of migrant and refugee flows in the 1970s and 1980s (Hatton 2012), coupled with demographic and security challenges in developing countries [START_REF] Geddes | Europe's Border Relationships and International Migration Relations[END_REF], started to significantly alter an international migration regime that was essentially based on the notion of 'control' [START_REF] Pécoud | Informing Migrants to Manage Migration? An Analysis of IOM's Information Campaigns[END_REF][START_REF] Georgi | For the Benefit of Some: The International Organization for Migration and Its Global Migration Management[END_REF]). In the 1990s, the collapse of the Soviet bloc and the wars in Iraq and the former Yugoslavia added further policy makers' concerns about the regulation of permanent and temporary migrations and refugee flows. A new regime, based on a global policy agenda relying particularly on the concept of 'migration management', was originally formulated by Bimal Ghosh, in 1993. Ghosh further developed this concept of 'migration management' in the 1996 project known as the New International Regime for Orderly international organization that would lead international cooperation on migration and refugee issues, based on humanitarian purposes, i.e., the United Nations High Commission for Refugees (UNHCR) [START_REF] Karatani | How History Separated Refugee and Migrant Regimes: In Search of Their Institutional Origins[END_REF]. In 1951, the conferences of Naples and Brussels ratified the US approach, which led to the creation of the PICMME, then re-christened several times before acquiring in 1989 the acronym IOM we know today. In short, Düvell argues that the IOM "was always intended to offer an economic counter-agency to the humanitarian UNHCR, set up the year before" (2003).

Georgi analyzes the historical development of the IOM in five major phases: during the cold war, the organization is a modest "anti-communist logistics agency" that supports some of western countries' migration policies. Secondly, from the 1980s to 1993, the organization experiences an opportunistic phase, in the context of globalization and the end of the Soviet bloc; from 1994 to 2000, an expansion by solving the 'migration control' problem with a 'migration management' solution, although Pécoud notes that the difference between control and management is extremely tenuous (2010,194); from 2000 to 2008, an exceptional growth of the IOM under Brunson McKinley's leadership; and from 2008 on, the IOM was in a post-neoliberal era (Georgi 2010, 49-61). We could also summarize this shift by suggesting that the IOM, originally a transport agency, shifted opportunistically to a multi-service agency for states.

The IOM, which is headquartered in Geneva, describes itself as a growing organization, from 67 member states in 1998 to 156 in 2014; from a total expenditure of US dollars (USD) 242.2 million in 1998 to USD 1.3 billion in 2013; IOM offices are located in more than 150 countries; operational staff was about 1,100 in 1998 and reaches at present 8,400, "almost entirely in the field" (IOM 2015g;Migreurop 2009). As opposed to numerous UN agencies that are going through significant organizational downsizing [START_REF] Hammerstad | The Rise and Decline of a Global Security Actor: UNHCR, Refugee Protection, and Security[END_REF], the IOM provides an interesting example of international organizations that have the wind astern, symptomatic of nation states' shifting international priorities in the 21 st century.

The expansion of the IOM, along with an increasing focus on border and migration security policy issues in diverse social science disciplines, may explain the emerging scholarly interest in this organization in the 2000s and 2010s. However, what explains the fact that it was and is still a relative research blind spot? First, the IOM is not an organization that belongs to the UN system.

The absence of the IOM in an organizational framework that is over-scrutinized by international relations students may thus explain in part this research myopia. Second, and this is related to the first point, due to its narrow mandate and limited resources and activities until the early 1990s, the IOM has been a marginal organization for decades, strived to reproduce itself, especially in the 1960s, when the 'iron curtain' threatened its existence (Georgi 2010, 51). Third, the IOM's lack of transparency regarding the services provided to its member states is another obstacle. Most of the contracts concluded by the IOM to offer these services are kept confidential. Besides, field research seems problematic: it is certainly possible to interview some IOM employees (see for instance Geiger 2010), and pretty challenging to converse with asylum seekers who are detained on the island of Lombok, east of Bali [START_REF] Ashutosh | Migration Management for the Benefit of Whom? Interrogating the Work of the International Organization for Migration[END_REF], but it is extremely difficult to interview temporary foreign workers who have signed an IOM contract and understandably fear reprisals for voicing concerns (see for instance Vargas-Foronda 2010a, Ancheita Pagaza and Bonnici 2013).

At least two topics seem to draw consensus among researchers who study the IOM. First, many scholars agree that the IOM fosters neoliberal values and policies in a globalized context [START_REF] Andrijasevic | The International Organization for Migration and the International Government of Borders[END_REF][START_REF] Geiger | The Politics of International Migration Management[END_REF]Vargas-Foronda 2010a). Similarly, Kalm uses the expression of 'neoliberal governmentality', borrowed from Foucault, which allows us to think about migration management in relation to the government of populations, where the maximization of human capital is seen as a key objective for governments and individuals (2010).

Not far from Kalm's analysis, Andrijasevic and Walters contend that the concepts of 'international liberalism' and 'global governmentality' allow us to grasp how the IOM works in a global field of power at the service of its member states; also, they argue that IOM policies should be analyzed through its practices, starting with specific ones defined by the IOM, for instance 'assisted voluntary return' (2010). Georgi identifies the IOM's political project as a form of "neoliberal global migration governance" (Georgi 2010, 67). Ashutosh and Mountz show how the IOM works "at the intersection of nation-states, international human rights regimes, and neoliberal governance" (2010,22).

Second, several scholars emphasize the fact that IOM activities also represent a significant business, relying for instance on EU funds, as the organization was able to secure European Commission funding to offer policy services to Albania (Geiger 2010, 157), on a vast repertoire of national ministries and agencies that consider that the IOM knows and defends migrants and asylum seekers' human rights (Pécoud 2010, 195;[START_REF] Geiger | Mobility, Development, Protection, EU-Integration! The IOM's National Migration Strategy for Albania[END_REF], or on temporary foreign workers' remittances (Vargas-Foronda 2010b).

In the context of this literature, the externalization and internationalization of migration management seems to be one of the core features of the current regime. Yet, this international migration management regime is increasingly questioned by scholars [START_REF] Geiger | The Politics of International Migration Management[END_REF]Kuntz et al. 2011) who have worked on the IOM. Although the literature proposes stimulating approaches to migration governance, it fails to propose a robust coherent framework that would make sense of the role of the IOM as a key component in the neoliberalizing processes we witness at multiple levels -local, national, transnational and international. In the first section of this chapter, we suggest an alternative model to analyze how neoliberal migration management requires focusing not only on the notions of workfare and prisonfare, but also on the 'theory of fields' theoretical framework. In this second section, we will analyze the role of the IOM in a labour contract for Guatemalan temporary foreign workers who are employed in farms in Canada.

Methodologically, this study relies on primary and secondary sources: primary sources include website pages from the IOM's main website, as well as contracts, appendices to contracts and documentation in Spanish provided by Jacobo Vargas-Foronda; secondary sources comprise scholarly, government, IGO and non-government organization (NGO) documents.

I. The role of the IOM in the field of 'borderfare'

Wacquant argues that, as opposed to neoliberalism analyzed from three main perspectives -i.e., one that can relate to an economist ideology, a mode of governance rooted in the notion of governmentality, and a repertoire of policy instruments -his view is restricted to a polarized approach: on the one hand, a monolithic economic approach that diverges into neoclassical and neo-Marxist declensions, and on the other, an unsteady use of the Foucaultian concept of governmentality. Nonetheless, Wacquant contends that both views of neoliberalism fail to make sense of the reshaping and unfolding of the state that anchors the norm of market rule into individuals' representations and social practices. In short, he argues that both conceptions are too "thin" for conceiving an "anthropology of neoliberalism": the economist approach is too restricted to the fantasy of markets, and does not take notice of broader non-economic dynamics; the governmentality perspective expands far beyond the economic domain, but does not clearly explain how technologies of conduct and norms are specifically neoliberal, how they flow, and how they structure the society (2012a).

Instead, Wacquant proposes to conceive neoliberalism as "market-conforming state crafting" (2012a, 71). By this, he means that the fundamental feature of neoliberalism is "an articulation of state, market and citizenship" (2012a, 71), and therefore proposes a "thick" sociological conception of neoliberalism that has three dimensions. The first one contends that neoliberalism, far from being an economic project, is a political one that is implemented, not by shortening sail, but by "reengineering the state". The second refers to the argument that neoliberalism shifts the "bureaucratic field" [START_REF] Bourdieu | Rethinking the state: on the genesis and structure of the bureaucratic field[END_REF]) -generally fitted with two wings, one that is both economic and penal, and one that is essentially social and protective, that struggle over the definition and distribution of public goods -toward the economic and penal one. This shift contributes to structure the state around two sets of policies, the first one analyzed as "workfare" policies by [START_REF] Peck | Workfare States[END_REF], the second that builds on this work by proposing the related notion of "prisonfare" [START_REF] Wacquant | Crafting the Neoliberal State: Workfare, Prisonfare, and Social Insecurity[END_REF](Wacquant , 2012b)). The third dimension refers to the expansion and praise of the penal wing of the state. Wacquant suggests that the penal apparatus is one of the core features of the neoliberal state, as the neoliberal state must deal with the consequences of neoliberal policies that generate social inequality, work instability and ethno-racial anxiety.

This redefinition of the neoliberal state from Wacquant will allow us to analyze how the IOM supports states that have implemented neoliberal reforms in several forms and degrees of intensity.

To do so, though, we will suggest two alterations to this foundational model: first, we will argue that the IOM undoubtedly serves states that implement workfare and prisonfare policies by using similar policy repertoires, but the added value of the IOM resides precisely in the fact that it offers a complementary set of externalized policies, entitled "border and migration management" by the organization, and that we call with a critical view "borderfare". The second alteration to this model is the use, not of the notion of the bureaucratic state that is limited to its two wings, but of the theory of fields (Fligstein andMcAdam 2011, 2012). The theory of fields draws partly on Bourdieu's work, solves some of Bourdieu's theoretical problems, and is at the same time more flexible in the sense that it can be used at the intersection of several fields -intergovernmental, transnational, national, local -and finally allows us to add a third wing to Wacquant's model. Thus, this section will be divided into sub-sections. The first one will focus on the field of borderfare. The second will analyze the IOM as an IGO that contributes to shape borderfare states.

The field of borderfare: Neoliberal migration control as a partial externalization of states' migration control

Analogous with the notions of workfare and prisonfare (Wacquant 2012b, 208), the concept of borderfare refers to the multilevel policy regime that addresses migration control problems by deploying militarized border patrols, offshore and domestic detention centres, domestic police forces and specialized courts, bilateral labour migration channels, along with their appendicesfor instance other ministries -private organizations, and IGOs such as the IOM. In other words, the borderfare regime offers a set of global solutions to block unwanted migrants and asylum seekers, and accept strictly what labour markets need in terms of temporary and permanent workers.

In order to explore this concept of borderfare further, we will use the theory of fields, the theoretical framework developed by Fligstein and McAdam, which they note is "an integrated theory that explains how stability and change are achieved by social actors in circumscribed social arenas" (2012,3). They suggest first to circumscribe the "strategic action field" (or field) that is studied, with the understanding that this field is not isolated, but closely linked with other fields. Fields are defined as "constructed social orders that define an arena within which a set of consensually defined and mutually attuned actors vie for advantage" (2012,64). In this sense, the field of borderfare allows to analyze the ways in which workfare and prisonfare take place, not just in domestic spaces, but also in multilevel and transnational spaces.

Fields are populated by three main categories of actors: first, incumbents "are those actors who wield disproportionate influence within a field and whose interests and views tend to be heavily reflected in the dominant organization of the strategic action field" (Fligstein and McAdam 2012, 13). In the field of borderfare, incumbents are nation states, although it might be more pertinent to suggest that only some nation states are incumbents in practice, namely the United States, that have considerable interests and resources regarding migration flows, along with other western countries. On the contrary, challengers "occupy less privileged niches within the field and ordinarily wield little influence over its operation. While they recognize the nature of the field and the dominant logic of incumbent actors, they can usually articulate an alternative vision of the field and their position in it" (Fligstein and McAdam 2012, 13). Challengers in the field of borderfare may be identified as the United Nations and its extensions, such as the UNHCR, the ILO and the United Nations Development Program (UNDP), as well as NGOs and trade unions that share an international human rights based view on migrations. Finally, internal governance units (IGUs) "are charged with overseeing compliance with field rules and, in general, facilitating the overall smooth functioning and reproduction of the system" (Fligstein and McAdam 2012, 13-14). IGUs in the borderfare field are the IOM that constructs neoliberal policies, practices and representations, as well as regional intergovernmental organizations, such as the International Centre for Migration Policy Development (ICMPD) and Frontex in Europe.

Fields are constantly in flux, and to understand the dynamics of strategic action, three stages of the field are identified: the field formation or emergence, which is one of the most challenging of the three states; the stable field that requires institutionalization and reproduction; and the field crisis that usually entails a resettlement of the field (Fligstein and McAdam 2012, 165-167). In the case of the borderfare field, the focus may be restricted to the field formation, and to the status quo. The emergence of the field of borderfare goes beyond the scope of this chapter, so we would only situate its stability around the 1990s-2000s, when a new migration regime is established to externalize the control of migrants, asylum seekers and migrant workers. Instead of controlling them only at the doors of each country, which appears to be increasingly difficult and entails several international and domestic legal obligations for some countries, new strategies are suggested to anticipate this control and elude those legal requirements: controlling them in their own country, which is equivalent to limiting the free movement of people and secluding categories of populations in their own country; controlling them when they are in transit, for instance by transport companies and by transit countries; and controlling them where they work, for instance in western countries. In this context, we will preferably use the notion of 'control' rather than the IOM's concept of 'management', as the latter is borrowed from a managerial semantic field meant to depoliticize and technicize migration control. This management newspeak is a key aspect of the neoliberal discourse, exemplified by Geiger who interviewed an IOM expert: "We have to move away from a control-oriented approach towards a proper, comprehensive and more managed approach to migration. A proactive way to look on migration not as a threat but as a benefit." (Expert interview, in Geiger 2010, 155).

The externalization of migration control follows this logic of internationalizing and transnationalizing such control. It consists in observing how states select migrants and asylum seekers, not just through national apparatuses, but increasingly through international or a combination of national and international, policy and administrative tools. A vast repertoire of multilevel administrative procedures is thus made available for the selection of permanent and temporary migrants and refugees, and based on several factors, essentially class, age, education/profession, race and gender, e.g., higher skilled labour migrants, lower-skilled labour migrants, seasonal workers, family migrants and asylum-seekers [START_REF] Geddes | Europe's Border Relationships and International Migration Relations[END_REF]. At the same time, the multiplicity of administrative tools tends to blur where states are and where they are not. In fact, the IOM is one of those international institutions that serve the nation states' neoliberal migration objectives, i.e., proposing tailored programs, communicating the hegemonic discourse on global migration management, eluding policy issues of human rights, and being opportunistically absent or present in the national and the international realms.

The IOM, a neoliberal migration agency that crafts 'borderfare' states

The IOM is a neoliberal migration agency that crafts borderfare states in two main directions: first, by moving the focus of a sociology of neoliberal states from the diptyque 'workfare-prisonfare' to the triptyque 'workfare-prisonfare-borderfare', it is possible to add an analytical layer that makes sense of the role of the IOM with its member states, hegemonic ones and subalterns. Secondly, the IOM is a 'centaur' organization that helps select migrants, refugees and workers.

From the Diptyque 'workfare-prisonfare' to the Triptyque 'workfare-prisonfare-borderfare'

The move from the diptyque 'workfare-prisonfare' to the triptyque 'workfare-prisonfareborderfare' with the theory of fields allows to consider the role of the IOM, mainly in the borderfare field, but also where the borderfare field intersects with the fields of workfare and prisonfare. In some instances, only two fields will intersect. For instance, although scholars critically analyze border and migration security practices (Dureau and Hily 2009;Ferrer-Gallardo 2008;Ferrer-Gallardo and Albet-Mas 2013), including the role of the IOM in their design and implementation [START_REF] Ashutosh | Migration Management for the Benefit of Whom? Interrogating the Work of the International Organization for Migration[END_REF], the IOM takes a slightly different stance: in a dedicated website entitled "Missing Migrants" (IOM 2015b), the IOM also denounces migrants' deaths, not to expose questionable security policies, but rather to distill fear and guilt in sending countries, as well as to keep delivering the narrative of an iron hand in a velvet glove to receiving countries. The IOM is here positioned at the intersection of the borderfare and the prisonfare fields. Namely, four stories illustrate migrants' tragedies: the lesson of one of those 'migrant experiences' is offered by Kessah, a young Ethiopian who sought to find better job opportunities in Saudi Arabia, and after encountering inexplicit but traumatic obstacles in his journey, was 'repatriated' to Ethiopia. Now, Kessah calls to sovereign powers to stop migrants; he emphatically passes on to others the (IOM) lesson he learnt, i.e., living in poverty in one's country should be celebrated: "My only dream now is that somebody may stop these 'trips' that are full of pain and suffering for poor people. This case, that could very well be fictional, illustrates how the IOM contributes to shape a rhetoric that seeks to use two types of registers, at the intersection of borderfare and prisonfare: the first one relates to the notion of 'symbolic violence' (Bourdieu 1998), used to internalize the prohibition of migrating illegally; in other words, would-be migrants would ideally refrain from using illegal migration channels, would try to use (inexistent or microscopic) legal channels, or would migrate to other countries. However, in parallel, this website is first and foremost accessible by first world countries that may take a humanitarian stance after reading these stories. This leads us to the second type of register mobilized by the IOM: first countries' citizens may consider that the IOM has a compassionate approach to migration. On this subject, Žižek contends that "compassion is the way to maintain the proper distance towards a neighbour in trouble" (Žižek 1994, 211). IOM's compassionate gaze towards migrants, a gaze that mainly originates from western countries, allows the avoidance of ethical concerns about those spaces of violence. This is precisely this compassionate gaze, according to Žižek, that reinforces the spaces and cycles of violence against migrants, through the quasi blanc-seing given to the IOM to control migrations, and consequently contributes to form borderfare states.

The IOM, a centaur organization to help manage centaur states' migrations

The IOM as a centaur organization helps in the selection of migrants, asylum seekers and temporary foreign workers (Wacquant 2012b). Namely, it is very liberal, laissez-faire and pleasant at the top of the hierarchy of the field, with employers and member states, and is conversely shortsighted, paternalistic and rude with those who are at the bottom: migrants, migrant workers and refugees.

The liberal approach of the IOM can be illustrated by [START_REF] Georgi | For the Benefit of Some: The International Organization for Migration and Its Global Migration Management[END_REF], who argues that the paradox of the IOM, using a positive, human rights-based discourse of migration that contradicts actions, policies and projects aimed at harsh migration control, is not the mere result of borrowing the international human rights narrative, as it was suggested by Human Rights Watch (HRW) (2003,2). Instead, the gap that exists between IOM's actions and rhetoric can be found in IOM's funding sources that tend to impose a migration control agenda, as opposed to the relative autonomy that the IOM can have as an international organization and growing, divided bureaucracy with a slightly different, human rights-oriented agenda (2010, 62). However, Pécoud contends that the use of a human rights rhetoric allows the IOM to be funded by a larger repertoire of ministries and agencies, not just home affairs and interior ministries, which tends to explain why the type of control suggested by the IOM is fairly ambivalent, "in-between control and humanitarian agendas" (2010,195). Besides, the borderfare field involves many different actors, and therefore must create a consensual policy agenda.

Conversely, the iron hand approach toward migrants and refugees can be observed through a complementary strategy of border security and migration management that consists of deploying an apparatus capable of intercepting migrants before they reach the territory of migration destination. There are also tools within receiving countries that detect illegal migrants through the collection of data by the welfare state, shared with border and migration departments. In addition, data can be collected by other actors, for instance actors from the private sector. Pécoud argues that "they rely on tools that have little to do with 'law and order', but rather with information technologies, communication and the media (newspapers, video clips, etc.)" (2010,195). Yet, we would argue that this data collection process has a lot to do with the remaking of 'law and order,' as it is a constitutive component of the silent techniques that allow pre-emptive and continuous targeted controls.

In addition, the IOM as a centaur organization helps manage specific centaur states' migrations.

The IOM has been instrumental in several aspects of the quantitative success of the Programa de Trabajo Agrícolas Temporal en Cánada (PTAT-C), which allows temporary labour migration between Guatemala and Canada, for instance in the selection of workers in Guatemala, and in the definition of the best route of the trip. First, the selection of workers is extremely discriminatory: the IOM, following the employers' desiderata, recruits essentially men who are on average 25 years old, married, along with other criteria [START_REF] Mantsch | Entrevistas directas abiertas sobre Canadá y Guatemala: Sus relaciones bilaterales y la Cooperación Canadiense en Guatemala[END_REF]):

It is not required that they know how to write. We have categories. If they need to work in the fields, they need to know how to add up, and even better if they know how to multiply.

With the Spanish, at least they can be understood. Depending on the type of crop, they need to have an understanding and experience with the type of work, and they do not need to be tall. We have different criteria for each type of job. Sometimes, they ask us that people be at least 1.65 meter tall, and in this case, we go to Oriente, Santa Rosa, Jutiapa, Progreso. Sometimes, they indicate to us that height does not matter, 1.40 or 1.50 meter. As for the gender, it is easier to get men than women. With them [women], a huge proportion cannot travel, due to a lack of identification documents, due to the fact that they are pregnant, they have kids, it is difficult to travel. As for the age, men must be already married, and even better if they have children. The Canadians consider that the average must be 25 years old, because people are more mature, they have plans, and for this reason they are more responsible, and thus have more opportunities [to be hired]. We have the experience that people between 19 and 20 years old, all of a sudden they realize that they earn a lot, they The experience of the IOM and the support of Guatemala's Ministerio de Relaciones Exteriores (MRE) are also useful in mapping out the best route of the trip between Guatemala and Canada, taking into account heightened border and migration security measures, promoted and implemented by other branches of the IOM and its most powerful member states. Initially, the trip to Canada passed in transit through the United States, but due to mistreatments suffered by Guatemalan workers, the route was changed to Mexico. Vargas-Foronda argues that, with MRE's assistance, it is fairly easy to get the Mexican transit visa, where it is possible to get a direct flight to Montreal (Vargas-Foronda 2010a, 25-26).

Secluding labour migrants: An example of IOM's compassionate mercenary business

This section examines how the IOM, when dealing with the business of sending Guatemalan for a "two-year pilot project", with 10 employers (IOM 2010). In 2010, the IOM claims that it was "assisting 1,000 migrants to travel to Canada" only in the month of June. For the whole year of 2010, the PTAT-C involved 14,000 migrants and 500 employers (IOM 2010). It has been expanding to other sectors, industry, services, and tourism [START_REF] Mantsch | Entrevistas directas abiertas sobre Canadá y Guatemala: Sus relaciones bilaterales y la Cooperación Canadiense en Guatemala[END_REF]. Nonetheless, the IOM has been increasingly excluded from the market of temporary foreign workers, due to the emergence of private firms, ironically made up by former IOM chiefs of mission and employees. This PTAT-C program is a stimulating case study for several motives: first, Guatemala and Canada never signed a bilateral agreement; second, private actors are involved in the foreground (private firms, Quebec employers, Guatemalan workers), but many public actors are present in the background (IOM, MRE, MTyPS, the former Human Resources and Skills Development Canada (HRSDC), Citizenship and Immigration Canada (CIC)); fourth, this case study exemplifies how the triptyque workfare-prisonfare-borderfare works in practice; finally, it demonstrates how the IOM is a centaur organization, which is particularly liberal and laissez-faire with Canadian employers, and very paternalistic and brutal with Guatemalan workers.

In order to analyze the role of the IOM in the PTAT-C, we will first examine how the IOM gained a leading role in this program, and then lost it at the end of the 2000s; we will then scrutinize a 2009 labour contract prepared by the IOM and another one prepared by a private firm in 2011, Amigo Laboral, managed by former IOM employees. Those contracts were signed between Guatemalan temporary workers and an association of Quebecois agricultural employers, la Fondation des Entreprises en Recrutement de Main-d'oeuvre agricole Étrangère (FERME).

The leading and fading role of the IOM in the PTAT-C program

It must be first noted that Canada and Guatemala have not signed a bilateral agreement in order to clarify the conditions under which the Guatemalan workers would be hired temporarily by Quebec agricultural employers. This is surprising for two reasons: on the one hand, a bilateral agreement exists between Canada and Mexico on the exact same matter, the Seasonal Agricultural Workers Program, established in 1974 with Mexico. This program has included Caribbean countries since 1966 on a bilateral basis as well, which means that extending it to Guatemala should not be difficult. On the other, the initiative of the program emanated from the MRE, which means that the MRE had the opportunity to construct and drive the program. However, the MRE sought to involve other actors, the MTyPS and the IOM. The MTyPS was brought to this initiative, as the Guatemalan labour legislation requires that Guatemalan workers, who sign a labour contract in Guatemala but work in another country, must be authorized by the MTyPS. At the same time, some actors involved in the process argue that the MTyPS had not the sufficient resources to pilot the program, e.g., recruiting (Coto Pineda 2010). However, the IOM had them, i.e., human, technical and financial resources (for instance, to cover the first workers' airline tickets in 2003, then reimbursed by FERME), to develop and implement the program. It was even argued that the IOM was especially interested in these issues, as it is in charge of them in Guatemala (Coto Pineda 2010, 2). A "Memorandum of Understanding for Technical Cooperation on Temporary Migrant Workers between the MTyPS and the IOM" was signed, according to the 2006 evaluation of the PTAT-C by the IOM, but the date and the text have not been made public yet (MRE, MTyPS and OIM 2006, 15). Finally, the construction of the program took place in IOM facilities in Guatemala, where MRE and MTyPS were invited. We can then observe here that the Guatemalan public administration had determined very early on that the IOM, which had already been a recipient of the externalization of these issues in Guatemala, should logically be the entity in charge of the PTAT-C. This project was created through an agreement between the IOM and FERME, under the supervision of HRSDC (MRE, MTyPS and OIM, 13), specifically an "MOU between FERME and the IOM in the Guatemalan Office of the IOM, for the implementation of the project of migrant workers to Canada", signed on July 10, 2003 (MRE, MTyPS and OIM, 14-16).

The failed strategy from the Guatemalan administration, or perhaps the posterior justification to legitimate the lack of leadership role in the PTAT-C, is summarized by a public servant from the MTyPS who was the assessor of the program in the 2000s: due to a basic lack of resources, the MTyPS decided to let the IOM take the reins, even if this implied to turn a blind eye to certain practices and provisions, in the perspective of taking the leadership later on and improving the conditions of the program for Guatemalan workers (Coto Pineda 2010). This did not happen, as the IOM sought to demonstrate that it managed a successful and growing program over the years (curiously, the 2006 evaluation was apparently carried out by the IOM itself, as well as by the MRE and the MTyPS), and as the MTyPS public servants eventually did not get the resources they expected. In addition, the IOM cannot assume a public administration role and lead the PTAT-C, since public administration cannot be delegated by the Guatemalan government, which would represent a breach of the Constitution of Guatemala, especially articles 154, 193 and 194 (Vargas-Foronda 2010a, 5). This may also reflect the influence of the IOM over the Guatemalan government and administration, and the fact that the IOM is a de facto governance entity in Guatemala, in charge of labour migration.

The lack of bilateral agreement between Guatemala and Canada, coupled with the lack of oversight from MRE, MTyPS, HRSDC and CIC, leads to a growing PTAT-C that allows extreme labour flexibility and abuse, as we will see below, in the examination of the contracts signed by Guatemalan workers. The growth of the program also emphasizes the fact that managing temporary migrant workers is a lucrative business, befitting relatively all actors involved: IOM Guatemala is congratulated for its good work by the IOM's hierarchy, Canadian employers are able to hire workers who are flexible and cheap; Guatemalan workers can earn several times what they can get in Guatemala (Coto Pineda 2010, 11), Canada recovers numerous taxes from temporary migrant workers and has very limited welfare expenses; remittances received by Guatemala are substantial, as they account for nearly 10 per cent of the GDP in 2013 (Pew Research Center 2013). Vargas-Foronda also shows that the IOM may benefit directly from remittances, sent by temporary foreign workers (TFWs) in Canada to their relatives: remittances in Canadian dollars go first to a BANRURAL account managed by the IOM, which are then transferred to BANRURAL accounts of migrants' relatives in Guatemalan Quetzales (2010a, 11).

Choosing BANRURAL is not contested, as the financial entity has numerous branches in rural areas in Guatemala. However, it is surprising that migrants' relatives are not allowed to manage their funds in Canadian dollars.

In 2011 this lucrative business led to the Chief of Mission of the IOM, a German, to establish a private business, the firm Amigo Laboral, managed by one of his relatives, and populated by former IOM employees. Amigo Laboral takes the Quebec market of migrant workers (the most important one), and leaves the Anglophone provinces to the next Chief of Mission, an American, who also soon created his own business to send Guatemalan workers to Anglophone provinces.

Ironically, this leaves the IOM, silent about those issues, without any market. However, the former Chiefs of Mission's mutual appetite leads them to compete. It is uncertain what the new IOM Chief of Mission for El Salvador, Guatemala and Honduras, who is from Latin America and studied in Europe (LinkedIn 2015), is going to do with the PTAT-C (Vargas-Foronda 2015, emails no. 1 and no. 2).

In practice, the PTAT-C, which is supposed to be mostly free for its applicants, involves a series of processes, detailed in the 2006 evaluation: a) Recruitment; b) Recruitment form process; c) Reception of required documents from worker and payment of fees; d) Visa application sent to embassy; e) Medical visit; f) How an application from a Guatemalan worker is processed; g) Allocation of application; h) Application to HRSDC (work permit); i) Visa granted; j) Conversation prior to the trip; k) Day trip; l) Worker's protection in Canada; m) Workers' return (MRE, MTyPS and OIM 2006, 17-20). The omission of the signature of the contract in this series of steps is not excessively surprising, given the condescending and paternalistic tone that is used throughout; in other words, the IOM does not specify when contracts are signed by migrant workers, and in fact we are not supposed to know that migrant workers sign a contract at any point, but we are led to understand that the contract is tacit. Another omission is the deposit of 4,000

Quetzales that each worker must make. Moreover, this series of processes is frequently challenged by former and current migrant workers (Vargas-Foronda 2010a). We will not be exhaustive here, and will only focus on a few ones, recruitment, mandatory deposit, and worker's protection in Canada.

First, recruitment is conducted by the IOM which uses databases and mappings of agricultural communities in Guatemala. Preliminary contacts and interviews are not announced by the IOM, as it claims that a public announcement can lead to abuses by IOM impersonators who charge a fee for nothing [START_REF] Mantsch | Entrevistas directas abiertas sobre Canadá y Guatemala: Sus relaciones bilaterales y la Cooperación Canadiense en Guatemala[END_REF]). As we have seen above, the recruitment follows several criteria, for instance gender, age, and height. But is also involves other requirements, for example physical condition (tests are conducted, for instance carrying a certain weight on a certain distance), limited literacy skills (illiteracy is rampant in rural areas where migrant workers are recruited), and professional skills (almost 70% of those who are interviewed are already working as small farmers for their own use, so that transferable skills can be detected easily) [START_REF] Mantsch | Entrevistas directas abiertas sobre Canadá y Guatemala: Sus relaciones bilaterales y la Cooperación Canadiense en Guatemala[END_REF], Vargas-Foronda 2010a, 7). Those criteria, requested by Canadian employers, and followed by the IOM, are clearly discriminatory and a breach of the Charte des droits et libertés de la personne du Québec, and the Canadian Human Rights Act.

Second, as opposed to what is described in the 2006 evaluation, migrant workers claim that a deposit is required by the IOM. The amount of 4,000 Quetzales must be deposited in one of IOM's accounts. Stefan Mantsch, in charge of the PTAT-C for the IOM, confirms that this deposit is required. If the worker does not have the entire amount, it can be paid in instalments, but it means that the bank has to lend this amount with a 15 to 30 per cent interest rate, which occurs for people who go to Canada for the first time. Next, Mantsch explains the reason why a deposit is required by the IOM:

The origin of this deposit is if the individual does not fulfil the contract. There are several conditions that specify when it is given back, and when it is not, it depends on the circumstances. [If they do not fulfil the contract] for motives like "I do not want to live here", "fellow workers bother me", "I do not like the food", and if they want to return because of this, with this deposit it is possible to send the worker who is going to replace him/her in Canada. This is the idea of the deposit (Mantsch 2009, 4 -translation by the author).

Besides the fact that this deposit appears to be purely and simply illegal, and does not constitute a potential compensation for the early termination of the contract, this deposit is never mentioned in the contract signed by migrant workers. Fortunately, if the contract is fulfilled, workers get their money back with a gain of one to three per cent interest (Mantsch 2009, 4).

Third, according to the 2006 evaluation, the worker's protection in Canada is supposedly held by the personnel of the "Consulate of Guatemala in Canada" (which is incorrect, and most likely refers to the Consulate General of Guatemala in Montreal, Quebec). This is surprising, as consulate personnel are not supposed to check the labour conditions of the country where they are posted. The protection of labour rights in Canada is generally the domain of federal and provincial governments, as well as trade unions. It must be noted that the Consulate welcomes migrant workers at the airport, and explains their rights and obligations in Canada. However, the Consulate does much more, as we discover in the 2006 evaluation:

In Canada, unions have contacted [Guatemalan workers] so that they join. They deceive them by saying that, if they join them, they will get better benefits from the employer. The work of the Consulate is to warn workers since the very moment they land in Canada, so that they know the existence of this labour organization, which will court them to offer services that the Consulate can offer for free. The constant communication and advising of the Consulate to the workers is the best way to avoid that these organizations trick them (Vargas-Foronda 2010a, 56). This anti-union rhetoric, found in a report co-written by the MRE, MTyPS and IOM, and in breach of several international and national conventions that recognize the right to unionize, is not so surprising. After all, the personnel of the Consulate seem to protect first and foremost the interests of the sending state, which is also one of the provisions of the same Vienna Convention, and certainly a superior injunction than the protection of its nationals. Thus, one of the migrant workers explains:

Those from the Consulate. They lead us to the boss, they talk about the wages, tell us that if the boss does not treat us well, we have to talk to them. They always come to the farm to see us, they ask 'How are you doing?', 'Are you working?', 'One must go to work, not waste time, not go for a walk' (Vargas-Foronda 2010a, 26).

The sentence arbitrale (arbitration award) that we will examine below shows that the Consulate was the organization the employer sought to contact in order to take disciplinary action against workers, and lay them off, which meant, for the Consulate, to send them back to Guatemala with zeal. The Arbitration Tribunal rejected this curious reading of the contract.

Labour contract between IOM/Workers-FERME

The copies of the contract we are going to examine have been gathered by Jacobo Vargas-Foronda.

The first one carries the logo of FERME. It is entitled "Contrato de trabajo de trabajadores agrícolas temporales de Guatemala en Quebec 2009," and has been signed by workers who were recruited by the IOM in order to work for FERME members (farm employers). The parties are the employer (with his exhaustive contact information) and the workers (listed in a separate appendix, "Lista de contractos de la finca," which includes the names, dates of contract, and signature of four workers). It is five pages long, and contains 24 articles. The second contract has been used in 2011 between the Guatemalan firm Amigo Laboral and FERME. The version we possess is not complete (2 pages long and until article 16), but it is clearly a carbon copy of the contract designed by the IOM: the same logo, wording, and structure, with only a couple of noticeable differences. For instance Appendix I has been simplified to include only the first name, last name and signature of each worker (the template allows up to six workers). Due to the fact that the second contract cannot be studied satisfactorily, we will limit our analysis to the first one, negotiated in 2009 by the IOM and FERME. Before examining the contract, we would like to emphasize the striking absence of any contract between the IOM and the Guatemalan workers who are recruited in the framework of the PTAT-C, which shows that the IOM acts as a quasi-MTyPS.

The IOM, followed from afar by the MRE and the MTyPS, took the lead, in the wording of this contract which has been used as a template by the IOM and FERME (Coto Pineda 2010); for instance, the balance between the contracting parties does not exist, but rather it is in the benefit of the employer (contracting parties, art. 22, signature section, Appendix I); the Consulate General of Guatemala in Quebec is wrongfully mandated "in all situations related to employment and stay" (art. 23); safety measures are barely mentioned (art. 3); information about holidays, conditions for being absent, psychological abuse is missing (art. 4-7).

The arbitration award we have mentioned earlier, between the union Travailleurs et travailleuses unis de l'alimentation et du commerce, section locale 501 (TUAC-FTQ) and an employer, seeks to solve allegations of lay off and discrimination against two Guatemalan workers, by scrutinizing the provisions of the contract and additional evidence. The allegations were received on December 21, 2009, and the arbitration award is dated December 11, 2014. The Arbitration Tribunal concluded that the employer laid off the complainants without just and sufficient cause, that the employer breached articles 10 and 16 of the Charte des droits et libertés de la personne following the complainants' discriminatory treatment based on their ethnic or national origin and language, and that the Tribunal is competent to determine compensation other than reinstatement. In this arbitration award, the role of the Consulate is stigmatized, as the Guatemalan diplomatic personnel sought to use their symbolic power in order to return Guatemalan workers promptly to Central America, although they have been discriminated against by their employer. In this context, the Consulate General of Guatemala is not just another actor in charge of the social control of migrant workers, at the intersection of workfare and borderfare: the Consulate, and more generally the MRE and the Guatemalan state, indicate that they follow IOM's neoliberal representations, policies and practices, even when this superior order negates international, Guatemalan and Canadian legislation.

But the contract is only one facet of the workers' obligations, as they receive additional instructions verbally and in writing: for example, Vargas-Foronda has gathered documents that have been used in 2010 by the IOM with Guatemalan workers sent to Alberta, one of them entitled "Informaciones para el día del viaje a Alberta, Canada", the other "Reglamento de normas y conductas en Alberta, Canada" (Vargas-Foronda 2010a). The second document includes some reminders set in bold typeface:

'Beware of relations with women, 2 Guatemalans have been detained for sexual abuse.' 'Important notice: when you arrive at the farm, the employer/ manager will keep your passport during your stay in Canada. In this way, you can be assured that it won't get lost.' 'Remember: you cannot compare yourself with Mexican workers, since they have other types of deductions.' (Vargas-Foronda 2010a) It is not possible to know whether these documents have also been handed out to Guatemalan workers in Quebec, but since they indicate clearly the same program (PTAT-C) administered by the IOM, it is likely that similar advice, rules and threats have been provided to all participants in the PTAT-C, in addition to the contract.

Altogether, the contract and these additional documents provide a context for considering another condition of workers' social control, this one lies at the intersection of the triptyque 'prisonfareworkfare-borderfare': workers are secluded in a farm / circumscribed area, where they are supposed to work as much as the employer wishes, under illegal labour conditions, and are threatened to return to Guatemala in disgrace and bearing the financial burden.

Conclusion

The field of borderfare allows connecting at the international and transnational levels the domestic fields of workfare and prisonfare. Within the field of borderfare, the IOM occupies the role of IGU, though its functions often overlap with the two other fields: for instance, when the IOM drafts the labour contract template of the PTAT-C, the IOM operates in the borderfare field to send temporary workers from Guatemala to Canada; also, the IOM acts in the workfare one, as workers fill unrewarding and underpaid jobs, though working in Canada is presented by the IOM as a privilege; finally, a euphemised prisonfare field intersects with the two other, as Guatemalan workers are confined to their workplace for several months, and face dire repercussions for not accepting it.

After this brief overview, several research agendas should certainly be explored: how do Canadian trade unions interact with temporary foreign workers in Quebec and in other provinces? How do they defend their rights? How is the judicial system used by temporary foreign workers? How is the IOM going to reassert its influence in Guatemala? Is it going to confront the migration services companies it generated at the end of 2000s, beginning of 2010s? What are the Guatemalan workers' paths during, after and between seasonal works in Canada?

These questions lead us to go back to what the IOM states on its websites: "[it] is dedicated to promoting humane and orderly migration for the benefit of all" (IOM 2015a). In this short sentence, the IOM is showing its contribution to the neoliberal project of its member states. Here, three brief comments should be made to scrutinize it. First, the assumption that this dual objective benefits all may be related to the notion that supporting a rational, progressive, modern neoliberal agenda is always justified, even though this agenda, backed by coercive means, creates spaces of violence, spaces of postcoloniality (Fanon 2004). Second, the apparent dilemma between "humane migration" and its opposing view, "orderly migration", might be solved by Althusser's idea of "ideological interpellation" or "hailing": an individual who walks on the street is suddenly hailed by a policeman; when this individual turns his head and looks at the policeman, this interpellation transforms the individual into a subject (Althusser 1970, 163). Similarly, the IOM's humane intervention works in such a way that migrants suddenly become subjects -subjects of an order that is beneficial to everyone, migrants and non-migrants. Naturally, the implicit fantasy is that migrants may not only become subjects of a broader order, but may be on a path to become superior subjects of this order, i.e., non-migrants. In other words, the IOM may be seen as the guardian of this order and the protector of migrants-as-subjects. Finally, if we follow Žižek, this IOM's regime might well be an additional illustration of "how ideology works" (Žižek 1989); by adopting a certain formulation of values and justice that is supported by human rights NGOs, IGOs, public opinion, as well as several categories of employees within the IOM, the organization and its member states are protecting us, comforting us, reassuring us. Simultaneously, they prohibit or

  My only truth now is to tell my friends about what happened to me and warn them not to go through what I went" (IOM 2015c).

  do not know what to do with this money, they do not have a vision, no plan, and for this reason, they want to return without fulfilling [their obligation]. People who are older have had better success(Mantsch 2009, 3 -translation by the author).

  temporary migrants to Quebec's farms from 2003 on, offers a compelling example of a compassionate mercenary at the service of states and employers. The PTAT-C was initiated in October of 2000, when the Embassy of Guatemala in Ottawa contacted the Guatemalan Ministerio del Trabajo y Previsión Social (MTyPS) and the IOM to follow up regarding the possibility of creating and managing a program to send Guatemalan temporary foreign workers to Quebec's farms (Comunicado del MRE número 100-2003, June 12, 2003, in Coto Pineda 2010, 2-3). It is assumed that the Embassy was either contacted by Canadian employers or acted based on its own evaluation of the Canadian labour market. The first groups of workers went to Quebec in 2003, 36 male workers in June, and 29 female workers in July. In total, 215 workers went to Quebec in 2003

1

  Dupeyron, Bruno. 2016. "Secluding North America's Migration Outcasts: Notes on the International Organization for Migration's Compassionate Mercenary Business." In Remote Control: The Externalization of Migration Management in Europe and North America, edited by Ruben Zaiotti, 238-258. Routledge Research in Place, Space and Politics. New York: Routledge.

limit the construction of alternative models for regulating migrations, thus contributing to maintaining the neoliberal status quo in the field it safeguards.

Delgado Wise, R., Márquez Covarrubias, H. and Puentes, R. 2013. Reframing the Debate on Migration, Development and Human Rights. Population, Space and Place. Vol.19, No.4, F. and Hily, 2009. Les mondes de la mobilité. Rennes: Presses Universitaires de Rennes. Düvell, F. 2003. The globalisation of migration control." In Open democracy -free thinking for the world. London: https://www.opendemocracy.net/peoplemigrationeurope/article_1274.jsp Fanon, F. 2004. The Wretched of the Earth, trans. Richard Philcox with commentary by Jean-Paul Sartre and Homi K. Bhabha, New York: Grove Press. Ferrer-Gallardo, X. 2008. The Spanish-Moroccan Border Complex: Processes of Geopolitical, Functional and Symbolic Rebordering. Political Geography. Vol. 27, No. 3, pp. 301-321. Ferrer-Gallardo, X. and Albet-Mas, A. 2013. EU-Limboscapes: Ceuta and the Proliferation of Migrant Detention Spaces across the European Union. European Urban and Regional Studies, November 11 2013. doi:10.1177/0969776413508766 Fligstein, N. and McAdam, D. 2011. Toward a General Theory of Strategic Action Fields. Sociological Theory. Vol. 29, No. 1, pp. 1-26. Fligstein, N. and McAdam, D. 2012. A Theory of Fields. New York: Oxford University Press. Foucault, M. 1976. Histoire de la folie à l'âge classique. Collection Tel 9. Paris: Gallimard. Foucault, M. 1978. The History of Sexuality Vol. 1: The Will to Knowledge. London: Penguin. Foucault, M. 2002. 'Society Must Be Defende': Lectures at the Collège de France, 1975-76, trans. David Macey, New York: Picador.


Denis Michel
email: denis.michel@live.fr

Source-receiver distances and redshifts inferred from luminosity distances under pure modes of expansion

Keywords: Space expansion, cosmological redshift, cosmological distances, informational horizon

Analytical relationships between source-receiver distances, redshifts and luminosity distances under pure modes of expansion

Introduction

The distance-redshift diagram initiated by Hubble [START_REF] Hubble | A relation between distance and radial velocity among extra-galactic nebulae[END_REF] is a central piece of information in cosmology, which can be envisioned as the black box of the universe in which are recorded the past modes of expansion. However, to allow using this diagram for deducing expansion rates, the measurements of the redshifts and distances should not have been experimentally correlated. Notably, deducing distances from redshifts would obviously introduce circular distortions in the reasoning. The distance used in the present study is the distance travelled by light, written D L . Among the different measurements of distances in astronomy, clearly summarized in [START_REF] Hogg | Distance measures in cosmology[END_REF], this distance is in theory equivalent to the luminosity distance, based on the decrease of apparent luminosity with distance of objects with known global luminosity. Be-cause of space expansion, D L is not the distance of the celestial body when the light was emitted since it was shorter, nor the actual distance because the space separating us from the star continued to expand during the time of travel of light. Hence, mathematical twists are necessary to connect distances to redshifts. These relationships are straightly established here without assuming a particular model. Instead of starting from Friedmann equations as usual, all cases of expansion will be examined using minimalist approaches applied to flat spaces devoid of gravitational influences. Let us begin with the basics: the origin of the redshift. [START_REF] Hogg | Distance measures in cosmology[END_REF] The main hypotheses on the origin of the redshift

Redshift without expansion

General relativity would be sufficient to cause distant objects to appear redshifted as a consequence of an apparent slowing of time. This attractive possibility will not be examined here, as space will be approximated as globally flat and not shaped by gravity. Another hypothesis, called "tired light", assumes that the longer is its flight, the more the light loses its energy by interaction with particles encountered along its path (which can originate from the quantum vacuum). As the tired light theory is not based on simple optical rules, it will not be treated here, but this theory curiously uses the same law as the simple exponential expansion [START_REF] Horedt | On the expanding-universe postulate[END_REF], which can of course give it a misleading success. This case will be indirectly treated when studying exponential expansion.

The redshift caused by expansion

The prevailing view is that the cosmological redshift is related to space expansion, but divergences exist about this relation. Two interpretations of the redshift, Doppler effect and wave stretching will be compared.

The redshift interpreted as a kinetic Doppler effect

The Hubble Redshift is frequently, perhaps erroneously, interpreted as a Doppler effect conceived conventionally (with a single light emission point but not as the addition of infinitesimal Dopper shifts along the light path postulated in the theory of [START_REF] Hogg | Distance measures in cosmology[END_REF][START_REF] Bunn | The kinematic origin of the cosmological redshift[END_REF]). An observer sees a red shift if the light source moved away from him when emitting the observed light. In case of expansion, the distant stars move away from each other, but passively. As mutually receding objects can belong to the same inertial reference frame, the question is whether a passive speed can generate a Doppler effect. With uniform motion, the redshift corresponding to the classical Doppler formula is z = V rec /c where V rec is the recession velocity and the relativistic redshift based on the Doppler formula of Einstein [START_REF] Einstein | Zur Elektrodynamik bewegter Körper (On the electrodynamics of moving bodies)[END_REF] is

z r = c + V rec c -V rec -1 (1)
This equation is little used in astrophysics in which recessional velocities can be superluminal (V rec > c) [START_REF] Davis | Superluminal recession velocities[END_REF]. In addition, this formula has been built in special relativity, whereas recession velocities V rec are generally supposed not uniform.

The redshift interpreted as a stretching of waves during their travel

Before the publication of Hubble [START_REF] Hubble | A relation between distance and radial velocity among extra-galactic nebulae[END_REF], Lemaître had shown that wavelengths should follow expansion [START_REF] Lemaître | Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques[END_REF]. For an interval of universe

ds 2 = dt 2 -a(t) 2 dσ 2 (2)
where dσ Is the element length of a space of radius equal to 1, the equation of a light beam is

σ 2 -σ 1 = t2 t1 dt a (3)
where σ 1 and σ 2 are the coordinates of a source and an observer. A beam emitted later at t 1 +δt 1 and arriving at t 2 + δt 2 undergoes a shift such that

δt 2 a 2 - δt 1 a 1 = 0 (4) giving z = δt 2 δt 1 -1 = a 2 a 1 -1 (5)
where δt 1 and δt 2 can be considered as the periods at emission and reception respectively [START_REF] Lemaître | Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques[END_REF]. In his article, Lemaître called this effect a Doppler effect. This term is acceptable if broadly defining the Doppler effect as a wave distortion, but this is not the classical Doppler effect related to the speed of the source. It will be shown here that both mechanisms give different results regardless of the type of expansion. In the wave stretching effect of Lemaître, the ratio between the reception and emission wavelengths simply follows the increase of the distance between the source and the receiver which took place during the light flight between the time point of emission (source and receiver spaced by D E ) and that of reception (source and receiver spaced by D R ):

λ app λ = D R D E (6a)
The corresponding redshift z s is the relative distance increase

z s = D R -D E D E or D R = D E (1 + z s ) (6b)
3 Relationships between Doppler effects and distance changes in uniform motion

The simple case of uniform motion is sufficient to perceive the symmetric nature of relative motion and the absence of a static medium and the mode of calculation of distance changes. Imagine that a source and a receiver can move relative to one another and in addition, can move relative to an hypothetical static medium supporting light propagation at speed c. The source and the receiver recede form each other at speed v. At time t E , when spaced from the receiver by D E , the source emits a light beam propagating towards the receiver.

In an immobile medium

Different results are obtained depending on whether this is the source or the receiver which moves relatively to the background medium (Fig. 1).

The receiver is considered immobile relative to the background medium

Light reaches the receiver at time t R after crossing a distance D E (bottom scheme of Fig. 1). Hence, the duration of the light travel is

t R -t E = D E /c (7a)
At t R , the new spacing between the source and the receiver has become

D R = D E + v(t R -t E ) (7b)
Replacing the duration in Eq.(7b) by its value given by Eq.(7a), yields a distance ratio corresponding to a classical Doppler effect

D R D E = 1 + v c (7c)
Distance increases in the same ratio that the classical Doppler effect. In case of collinear approach, the same reasoning gives

D R D E = 1 - v c (7d)

The source is considered immobile relative to the background medium

In this case, light is expected to reach the receiver after crossing a distance D R (middle scheme of Fig. 1). The duration of the light travel is

t R -t E = D R /c (8a)
Replacing the duration in Eq.(7b) by its value given by Eq.(8a), yields a conjectural Doppler formula

D R D E = 1 1 - v c (8b)
In case of collinear approach, the same reasoning gives

D R D E = 1 1 + v c (8c)
These contradictory results suggest that the notion of immobility in a static space should be ruled out. Interestingly, the geometric means of the two extreme results obtained by postulating the static medium (Eqs (7c)/(8b) and Eqs (7d)/(8c)), is the relativistic Doppler effect. For the recession:

D R D E = c + v c -v (9a)
and for the approach

D R D E = c -v c + v (9b)

Without background medium

In the special relativity theory, uniform motion cannot be attributed specifically to one of the relatively moving frames. The total distance crossed by light is not D R nor D E , but

D L = c(t R -t E ) = c v (D R -D E ) ( 10
)
The precise relationships between D R , D E and D L will be calculated later. These simple considerations suggest that a relative speed of light should be defined, not bound to the source or the receiver.

Definition of a relative speed of light

For light following geodesics (s = 0), the metric of Friedmann-Robertson is very simple. By rewriting the interval of Eq.( 2) in Cartesian coordinates, this metric reads

ds 2 = (cdt) 2 -a(t) 2 (dx 2 + dy 2 + dz 2 ) ( 11
)
where a(t) is the spatial expansion factor depending on time only [START_REF] Einstein | On the relation between the expansion and the mean density of the Universe[END_REF]. For a light beam oriented along the x axis, this line element reduces to

dx dt = c a(t) . (12)
The ratio would be equivalent to a relative speed if adding a unit of distance to a(t). Accordingly, a time -1 equation is obtained with the Friedmann-Lemaître-Robertson-Walker approach giving dχ/dt = c/a(t) where χ is an angle (without dimension) and a(t) is a distance, more appropriately written R(t) in this case.

Influence of expansion on signal connection

The relative speed of light and expansion could limit or even forbid the connection between sources and receivers. Let us examine precisely the different cases of expansion.

Uniform expansion

Several authors have suggested a mode of universe expansion called a ∝ t, which simply follows the cosmic time [START_REF] Vigoureux | A New cosmological model[END_REF][START_REF] Cook | Interpretation of the cosmological metric[END_REF][START_REF] Melia | The Rh=ct Universe[END_REF]. When a(t) = ct, ȧ = c and H = 1/t, expansion follows the age of the universe according to

D(t) D E = t t E (13)
In fact, with a linear cosmic time, this expansion simply corresponds to the uniform expansion at constant speed v. Indeed, Eq.( 13) can be re-written

D(t) D E = 1 + t -t E t E (14a)
or

D(t) = D E + D E t E (t -t E ) (14b) that is D(t) = D E + v(t -t E ) (14c)
Uniform expansion means at constant intervals, but not necessarily slow expansion, as the speed can be unlimited. With uniform expansion and given sufficient time, a walker will inevitably cross a road even if stretching at gigantic superluminal speed, whatever his walking speed (eg walk at c = 4 km/h while the road stretches at v = 1,000 km/h). This result is so counterintuitive that it has been popularized as a mathematical game [START_REF] Gardner | Time travel and other mathematical bewilderments[END_REF]. The relative speed (time -1 ) can be written in two manners using the correspondence

D(t) = D E (t/t E ) = D E + vt, dx(t) dt = ct E D E t = c D E + vt (15)
whose integration gives a unitless relative position x, starting from x(t E ) = 0, of

x(t) = ct E D E ln t t E = c v ln 1 + vt D E (16)
These functions without ceiling indicate that the walker continues its merry way and necessarily reaches the other end of the screen (when x(t) = 1), even with a very high stretching rate v. If the walker is a photon, signals cannot be disconnected in the universe. The journey can however be very long as its duration follows

∆t = D E v (e v/c -1) (17)
Whatever the relative values of v and c, there is no disconnection between the different parts of this universe. To try to interrupt this connection, one must change the mode of stretching. Let us examine first a mode of expansion widely used in astrophysics, the geometric progression called "power law".

Power law expansion

This mode of expansion, predicted by calculations based on the theoretical constituents of the universe, satisfies

D(t) = D E t t E u ( 18
)
where u can take different values depending on the maturation stage of the universe described in astrophysics courses: 1/2 for the radiation-dominated era, 2/3 for the matter-dominated era, 1/3 for the stiff fluid, u = 2 for a minimal condition of inflation satisfying ä/a > 0, etc. The relative position of the walker (photon) is obtained by integration between t E and t

x(t) = t τ =tE c D E τ t E -u dτ = c (1 -u) t E D E t t E 1-u -1 (19)
Things get interesting:

-(i) For u < 1, x(t) increases continuously with t and therefore can exceed 1 without problem. As for the previous modes of expansion, the universe is revealed in its entirety though at different ages.

-(ii) For u > 1, information cannot cross a virtual limit called horizon

x(t ∞ ) = c t E D E (u -1) (20)
The success of the connection depends on the initial conditions of light emission: the time of departure (t E ) and the distance to be covered as it is at this time (D E ). Now let us try another accelerated mode of expansion in which time is not raised to a power, but is itself an exponent: the exponential expansion.

Exponential expansion

With an exponential expansion of rate H, the initial distance stretches according to D(t) = D E e H∆t and the relative speed of light is

dx(t) dt = c D E e -H(t-tE) (21)
whose integration between t E and t, gives his relative position on the source-receiver spacing unit.

x(t) = c HD E 1 -e -H∆t (22)
This position tends asymptotically to a maximum c/HD E , which means that for given values of H and c, the success of the connection depends on D E . To reach the goal, c/HD E must exceed 1, so D E must be lower than c/H. The critical distance c/H is a disconnection point in the expanding universe, that is unreachable because the time of travel

∆t = 1 H ln    1 1 - HD E c    (23)
would become infinite, and at t infinite, the relative speed dx(t)/dt is zero. This distance is universal in a homogeneously expanding universe and valid from any starting point.

Consequence of the Hubble law V rec = HD

The proportionality between the recession velocity and the distance can be written dx/dt = Hx, where H is the slope of a straight line. As the slope of a straight line is a constant, the unique solution of the Hubble law is x(t) = x(0)e Ht . This expansion is not only a model (of de Sitter), but also just the only possible mathematical solution of V rec = HD, as long as H is constant. It is recommended to write V rec = H 0 D to clearly indicate that H(t) may have been different in the past. Interesting questions are: how much of the universe we can see and how far we have to look for seeing a H different from H 0 .

Specificities of the exponential mode of expansion -(i) It is an infinite mode of expansion without big

bang, because a(t) = a 0 e Ht (Hubble law) has no root, so a universe steadily submitted to exponential expansion has always existed. The absence of an original singularity is particularly interesting in the case of an infinite universe, because getting an infinite space by stretching a finite space is a pure mathematical impossibility.

-(ii) This mode of spatial expansion is that of the flat version of the universe of de Sitter [START_REF] De Sitter | The expanding universe[END_REF] (for k = 0), towards which converge at long times the positively curved version (x(t) = x(0) cosh Ht for k = 1), and the negatively curved version (x(t) = x(0) sinh Ht for k = -1). After a period of success, the model of exponential expansion of de Sitter was disqualified because it has been shown to not satisfy theoretical predictions based on assumptions of pressure and density of the universe. It is however supposed to be the present mode of expansion driven by vaccum energy since we entered the "dark energy-dominated era" in which H 0 is a constant H 0 = Λ/3, where Λ is the cosmological constant.

5 Tools and observables

Nomenclature

The traditional nomenclatures should be adapted to cosmology in which the suffix 0 is not used for the initial condition as in most usual treatments, but for the final condition (present). The following symbols are therefore used to avoid misunderstanding:

-t E is the date of light emission (initial, generally written t 0 in other scientific contexts). This date can not be measured directly. -t R is the date of reception of the light (final). This is the present age of the universe, written t 0 by cosmologists. Of course if running time backward, an acceleration becomes a deceleration and vice versa, which may induce some misunderstandings. -D E is the initial distance between the star and the telescope (which did not exist yet!) at t E . D E is not known a priori. -D R is the distance between the source and the telescope when light enters it. -D L is the distance travelled by light between its emission and its reception. Hence,

D L /c = t R -t E .
D L is smaller than D R because the fraction of space already crossed by light continued to stretch until reception. The measurement of D L is simple, at least in its principle. In a flat 3D space, a source emitted light in all the directions so that the light front progressively increases as the surface of a sphere 4πD 2 where D = ct. As a consequence, the flux of light I detected by an observer at the surface of this sphere corresponds to the 1/4πD 2 th of the total light I tot emitted by the celestial body when it was as it appears in the telescope after redshift correction, giving

D = I tot /4πI
This distance is not based on z, even if z is used in practice to assist the measurement, for correcting energy and selecting the range of observable wavelengths to consider. Type Ia supernovae are particularly appropriate for measuring distances by this way given their standard brightness, which greatly helped refining the distance-redshift diagram in the last decades [START_REF] Perlmutter | Nobel Lecture: Measuring the acceleration of the cosmic expansion using supernovae[END_REF].

Quantities measurable in our telescopes

In the theory of Lemaître, the redshift is given by the ratio D R /D E (Eq.( 6)), but none of these distances is directly measurable, contrary to the distance crossed by light (D L ). Note that the same light received at t R is used to measure both the redshift and the distance.

Additional recipes

t R , the present age of the universe, is not known but can be replaced by a constant because it is common to all our measurements. Finally, a very useful tool is the fractional distance x(t) crossed by the front of light between the transmitter and the receiver, defined by the function

x(t) = t τ =tE c D(τ ) dτ
where D is the source-receptor distance. Then, the date of arrival t R is simply obtained by solving

x(t R ) = 1
6 Redshift-Distance relationships expected for the different modes of expansion

Let us examine successively the different modes of expansion and for each one, the two hypothetical causes of redshift : Doppler effect and wave stretching.

Power-law expansion

D E = D R t E t R u (24a)
The speed of the source at emission can be deduced from the distance at reception

z d = 1 c dD E dt E (24b)
that is, taking D R and t R as constants

z d = uD R c t u-1 E t u R = uD E ct E (24c)
replacing t E by t R -D L /c and D R or D E by their values deduced from x(t R ) = 1,

z d = u 1 -u 1 - D L ct R u-1 -1 (24d)
where t R can be considered as a constant at our time scale.

Wave stretching

The result is straightforward

D R D E = t R t E u = 1 - D L ct R -u (25a)
and

z s = 1 - D L ct R -u -1 (25b)
6.2 The particular case u = 1 (a ∝ t)

As explained previously, this case merely corresponds to uniform expansion.

Doppler effect

Classical Doppler effect

The recession velocity for this mode of expansion is simply D/t, where D and t vary proportionally,

D E t E = D R t R = v
and

z d = v c (26)
which supports superluminal velocities.

Relativistic Doppler effect Using special relativity, the redshift is

z r = c + v c -v -1 (27)

Wave stretching

By definition for this mode of expansion,

λ app λ = D R D E = t R t E (28)
and by solving

x(t R ) = 1, t R t E = e DR/ctR = e v/c (29)
and

z s = e v/c -1 (30)
The two postulated causes of redshift give different results, which are similar only near 0 (for v << c). Both predict distance-independent redshifts, which clearly disqualifies this mode of expansion.

Exponential expansion

Doppler effect

Classical Doppler effect

The speed of the source at the time of light emission is

dD E dt = HD E ( 31
)
whose value is obtained by solving x(t R ) = 1,

z d = HD E c = 1 -e -HDL/c (32)
As z d is always lower than 1, the hypothesis that the redshift exclusively results from a classical Doppler effect can be eliminated for the exponential expansion.

Relativistic Doppler effect

z r = c + HD E c -HD E -1 (33)

Wave stretching

The wavelengths are stretched according to

λ app λ = D R D E = e H∆t = e HDL/c (34) so that
z s = e HDL/c -1 (35a)
whose reciprocal is

D L = c H ln(1 + z s ) (35b)

Mixing Doppler and stretching effects for the exponential expansion

The above results can be combined in a variety of manners. Let us examine only the case of the exponential expansion. The Doppler and wave stretching redshift functions established above display opposite behaviors near 0, clearly visualized by their series expansion. For the classical Doppler effect,

z d ≈ H 0 D L c - 1 2
H 0 D L c 2 (36a)
and for the wave stretching effect,

z s ≈ H 0 D L c + 1 2
H 0 D L c 2 (36b)
Hence, by comparison with the traditional redshift formula z = H 0 D/c, the Doppler effect seems to include an acceleration parameter, while the wave stretching effect seems to contain a deceleration parameter. For nearby galaxies, the so-called peculiar or ordinary velocities can not be neglected because they can either increase, decrease or cancel the cosmological redshift. Generally, the task of astrophysicists is difficult to disentangle the different interfering sources of redshift, including gravity and peculiar velocities, and to determine the specific contribution of expansion [START_REF] Harrison | The redshift-distance and velocitydistance laws[END_REF]. These technical problems however demonstrate that several causes of redshift can actually interfere. After all, a recession velocity, though passive, remains a velocity and as such, one wonders why it could not give a kinetic Doppler effect contributing to the redshift. Hence, for completeness and by curiosity, let us cumulate the two effects. In addition to take the two hypotheses on the origin of the redshift into account, two ways to bring them together will be considered.

Combined effects

Assuming, on the one hand, that the dilation of wavelengths caused by kinetic Doppler effect (λ dopp ) is fixed at the emission point and then remains unchanged during light flight and assuming, on the other hand, that the emission wavelength is expanded during the trip, until received in the form λ app , the cumulative effect would logically read

λ app λ = λ app λ dopp λ dopp λ ( 37
)
using the classical Doppler effect,

z d+s = (1 + z d )(1 + z s ) -1 = 2z s (38)

Additive effects

As wavelengths are lengths, they should perhaps be handled as such. Adding the relative length increase caused by Doppler effect z d and that caused by stretching z s gives

z d+s = z d + z s (39)
Using the classical Doppler effect, z d+s = e HDL/ce -HDL/c = 2 sinh The redshift of dual origin of Eq.(40) gives a straighter redshift-distance diagram compared to its individual components (clearly illustrated by the cancellation of the squared terms in Eq.( 36)). But if for some reason the Doppler effect predominates for nearby galaxies, a bend would appear in the Hubble diagram for low redshifts, mimicking a recent acceleration for galaxies of redshift below unity. A simple function describing such hypothetic situation is z = 2 sinh(x)/(1 + x) with x = HD L /c. Its comparison with the observed redshifts of supernovae compiled in [START_REF] Riess | Type Ia supernova discoveries at z > 1 from the Hubble Space Telescope: evidence for past deceleration and constraints on dark energy evolution[END_REF], is represented in Fig. [START_REF] Hogg | Distance measures in cosmology[END_REF], drawn in linear coordinates because a logarithmic scale is poorly appropriate to visualize the straightness of a linear plot. This exercise of redshift addition at H 0 constant is purely formal because the accepted explanation of this bend is a recent change of H driven by dark energy [START_REF] Perlmutter | Nobel Lecture: Measuring the acceleration of the cosmic expansion using supernovae[END_REF].

HD L c (40)

Distance of a source inferred from its apparent distance

The observed distance of cosmic objects (D L ) does not correspond to any real distance, but the actual distances can be deduced from this measured distance provided a mode of expansion is selected.

-For the uniform expansion:

Since D L = c∆t, Eq.( 17) gives

D E = D L v/c e v/c -1 (41a) and since D R = D E + v∆t, D R = D L v/c
1 -e -v/c (41b)

These distances satisfy both the established distances relationship of Eq.( 10) and the stretched shift of Eq.( 30).

-For the geometric expansion:

When x(t R ) = 1, Eq.( 19) gives

D E = ct R -D L 1 -u 1 - D L ct R u-1 -1 (42a) so that D R = ct R 1 -u 1 -1 - D L ct R 1-u (42b)
-For the exponential expansion:

When x(t R ) = 1, Eq.( 22) gives

HD E = c 1 -e -H∆t

Conclusion

This study expands that of Harrison [15] which rationally derived the links between redshift and distance in a purely mathematical manner depending on the type of expansion. A series of conclusions can already be drawn: For exponential expansion, the traditional redshift formula z = H 0 D/c is close to z s = e H0DL/c -1 only in the vicinity of D = 0 and z = H 0 D/c is valid only for the invisible actual distance D R but not for the luminosity distance D L . Whatever the expansion modes, the two postulated origins of the redshift: conventional Doppler and wave stretching effects, always give different results, as stated by Harrison [START_REF] Harrison | The redshift-distance and velocitydistance laws[END_REF]. The mere existence of redshifts higher than 1 is sufficient to rule out the Doppler effect as the sole cause of redshift in the case of the exponential expansion. Finally, the present calculations show that the only two modes of expansion which are capable of generating disconnection barriers, are the exponential expansion (Horizon at D E = c/H) and the geometric expansion if u > 1 (Horizon at D E = ct E /(u -1)).

Table 1 -Summarized consequences of the modes of expansion on the redshift, the horizon and the source-receiver distances. V rec is the apparent source velocity at emission. z d and z s are the redshifts calculated as Doppler or wave-stretching effects respectively. D E is the source-receiver distance at emission, D R is the source-receiver distance at reception and D L is the apparent distance actually measured. t R is the present time, which can be approximated as a constant as it is identical for all our measurements.

Mode

a ∝ t (u = 1) Power law (u = 1) Exponential

D(t) = D E t t E D E t t E u D E e H(t-tE) ȧ a 1 t u t H Horizon No u < 1 : No u > 1 : for D E ≥ c t E u -1 for D E ≥ c H V rec D t = v uD E t E HD E z d v c u 1 -u 1 - D L ct R u-1 - 1
1 -e -HDL/c

z s e v/c -1

1 - D L ct R -u
-1

e HDL/c -1

D E D L v/c e v/c -1 ct R 1 -u 1 - D L ct R 1 - D L ct R u-1 -1 c H 1 -e -HDL/c D R D L v/c 1 -e -v/c ct R 1 -u 1 -1 - D L ct R 1-u c H
e HDL/c -1

Figure 1 .

 1 Figure 1. A light pulse is emitted by a source (S) when spaced from a receiver (R) by DE. Just like a ball thrown between two football players, light travels through a static medium relatively to which either S (middle line) or R (bottom line), is considered immobile.

6. 1 . 1

 11 Classical Doppler effect

Figure 2 .

 2 Figure 2. Speculative curve fitting of the distance-redshift supernovae distribution (dots) with an exponential expansion model in which the Doppler effect predominates at short distances while wave stretching predominates at long distances (plain line). The redshift data are from [16] and include 186 supernovae. The fitting parameters are c = 3 × 10 8 m/s and H = 3.23 × 10 -18 /s, a poorly precise value due to the conversion of Distance modulus (µ) in a non-logarithmic scale using the relationship DL = 10 1+µ/5 10 -6 Mpc.