2.1 Introduction

The identification of dark matter is one of the most important open problems in particle physics and cosmology. In standard cosmology, dark matter contributes 85% of all the matter in the universe, but we do not know what it is made of, as we have never observed dark matter particles in our laboratories. The foundations of the modern dark matter paradigm were laid in the 1970s and 1980s, after decades of slow accumulation of evidence. Back in the 1930s, it was noticed that the Coma cluster seemed to contain much more mass than what could be inferred from visible galaxies [992, 993Jump To The Next Citation Point], and a few years later, it became clear that the Andromeda galaxy M31 rotates anomalously fast at large radii, as if most of its mass resides in its outer regions. Several other pieces of evidence provided further support to the dark matter hypothesis, including the so called timing-argument. In the 1970s, rotation curves were extended to larger radii and to many other spiral galaxies, proving the presence of large amounts of mass on scales much larger than the size of galactic disks [712].

We are now in the position of determining the total abundance of dark matter relative to normal, baryonic matter, in the universe with exquisite accuracy; we have a much better understanding of how dark matter is distributed in structures ranging from dwarf galaxies to clusters of galaxies, thanks to gravitational lensing observations [see 644, for a review] and theoretically from high-resolution numerical simulations made possible by modern supercomputers (such as, for example, the Millennium or Marenostrum simulations).

Originally, Zwicky thought of dark matter as most likely baryonic – missing cold gas, or low mass stars. Rotation curve observation could be explained by dark matter in the form of MAssive Compact Halo Objects (MACHOs, e.g., a halo of black holes or brown dwarfs). However, the MACHO and EROS experiments have shown that dark matter cannot be in the mass range −7 0.6 × 10 M ⊙ < M < 15M ⊙ if it comprises massive compact objects [23, 889]. Gas measurements are now extremely sensitive, ruling out dark matter as undetected gas ([134, 238, 765]; but see [728]). And the CMB and Big Bang Nucleosynthesis require the total mass in baryons in the universe to be significantly less that the total matter density [759, 246, 909].

This is one of the most spectacular results in cosmology obtained at the end of the 20th century: dark matter has to be non-baryonic. As a result, our expectation of the nature of dark matter shifted from an astrophysical explanation to particle physics, linking the smallest and largest scales that we can probe.

During the seventies the possibility of the neutrino to be the dark matter particle with a mass of tenth of eV was explored, but it was realized that such light particle would erase the primordial fluctuations on small scales, leading to a lack of structure formation on galactic scales and below. It was therefore postulated that the dark matter particle must be cold (low thermal energy, to allow structures on small scale to form), collisionless (or have a very low interaction cross section, because dark matter is observed to be pressureless) and stable over a long period of time: such a candidate is referred to as a weakly interacting massive particle (WIMP). This is the standard cold dark matter (CDM) picture [see 369, 719].

Particle physicists have proposed several possible dark matter candidates. Supersymmetry (SUSY) is an attractive extension of the Standard Model of particle physics. The lightest SUSY particle (the LSP) is stable, uncharged, and weakly interacting, providing a perfect WIMP candidate known as a neutralino. Specific realizations of SUSY each provide slightly different dark matter candidates [for a review see 482Jump To The Next Citation Point]. Another distinct dark matter candidate arising from extensions of the Standard Model is the axion, a hypothetical pseudo-Goldstone boson whose existence was postulated to solve the so called strong CP problem in quantum chromodynamics [715Jump To The Next Citation Point], also arising generically in string theory [965, 871Jump To The Next Citation Point]. They are known to be very well motivated dark matter candidates [for a review of axions in cosmology see 826Jump To The Next Citation Point]. Other well-known candidates are sterile neutrinos, which interact only gravitationally with ordinary matter, apart from a small mixing with the familiar neutrinos of the Standard Model (which should make them ultimately unstable), and candidates arising from technicolor [see, e.g., 412]. A wide array of other possibilities have been discussed in the literature, and they are currently being searched for with a variety of experimental strategies [for a complete review of dark matter in particle physics see 51].

There remain some possible discrepancies in the standard cold dark matter model, such as the missing satellites problem, and the cusp-core controversy (see below for details and references) that have led some authors to question the CDM model and to propose alternative solutions. The physical mechanism by which one may reconcile the observations with the standard theory of structure formation is the suppression of the matter power spectrum at small scales. This can be achieved with dark matter particles with a strong self-scattering cross section, or with particles with a non-negligible velocity dispersion at the epoch of structure formation, also referred to as warm dark matter (WDM) particles.

Another possibility is that the extra gravitational degrees of freedom arising in modified theories of gravity play the role of dark matter. In particular this happens for the Einstein-Aether, TeVeS and bigravity models. These theories were developed following the idea that the presence of unknown dark components in the universe may be indicating us that it is not the matter component that is exotic but rather that gravity is not described by standard GR.

Finally, we note that only from astrophysical probes can any dark matter candidate found in either direct detection experiments or accelerators, such as the LHC, be confirmed. Any direct dark matter candidate discovery will give Euclid a clear goal to verify the existence of this particle on astrophysical scales. Within this context, Euclid can provide precious information on the nature of dark matter. In this part, we discuss the most relevant results that can be obtained with Euclid, and that can be summarized as follows:

Finally, Euclid will provide, through gravitational lensing measurement, a map of the dark matter distribution over the entire extragalactic sky, allowing us to study the effect of the dark matter environment on galaxy evolution and structure formation as a function of time. This map will pinpoint our place within the dark universe.

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