The field is rich in UDM models [see 128, for a review and for references to the literature]. The models can grow structure, as well as providing acceleration of the universe at late times. In many cases, these models have a non-canonical kinetic term in the Lagrangian, e.g., an arbitrary function of the square of the time derivative of the field in a homogeneous and isotropic background. Early models with acceleration driven by kinetic energy [-inflation 60, 384, 154] were generalized to more general Lagrangians [-essence; e.g., 61, 62, 795]. For UDM, several models have been investigated, such as the generalized Chaplygin gas [488, 123, 137, 979, 741], although these may be tightly constrained due to the finite sound speed [e.g. 38, 124, 784, 985]. Vanishing sound speed models however evade these constraints [e.g., the silent Chaplygin gas of 50]. Other models consider a single fluid with a two-parameter equation of state [e.g 74]), models with canonical Lagrangians but a complex scalar field [55], models with a kinetic term in the energy-momentum tensor [379, 234], models based on a DBI action [236], models which violate the weak equivalence principle [375] and models with viscosity [321]. Finally, there are some models which try to unify inflation as well as dark matter and dark energy [206, 688, 572, 575, 430].

A requirement for UDM models to be viable is that they must be able to cluster to allow structure to form. A generic feature of the UDM models is an effective sound speed, which may become significantly non-zero during the evolution of the universe, and the resulting Jeans length may then be large enough to inhibit structure formation. The appearance of this sound speed leads to observable consequences in the CMB as well, and generally speaking the speed needs to be small enough to allow structure formation and for agreement with CMB measurements. In the limit of zero sound speed, the standard cosmological model is recovered in many models. Generally the models require fine-tuning, although some models have a fast transition between a dark matter only behavior and CDM. Such models [729] can have acceptable Jeans lengths even if the sound speed is not negligible.

An action which is applicable for most UDM models, with a single scalar field , is

where and indicates covariant differentiation. This leads to an energy density which is , and hence an equation-of-state parameter (in units of ) given by and . A full description of the models investigated and Lagrangians considered is beyond the scope of this work; the reader is directed to the review by [128] for more details. Lagrangians of the form where is a Born–Infeld kinetic term, were considered in a Euclid-like context by [201], and models of this form can avoid a strong ISW effect which is often a problem for UDM models [see 127, and references therein]. This model is parameterized by a late-time sound speed, , and its influence on the matter power spectrum is illustrated in Figure 44. For zero sound speed CDM is recovered.Of interest for Euclid are the weak lensing and BAO signatures of these models, although the supernova Hubble diagram can also be used [885]. The observable effects come from the power spectrum and the evolution of the equation-of-state parameter of the unified fluid, which affects distance measurements. The observational constraints of the generalized Chaplygin gas have been investigated [706], with the model already constrained to be close to CDM with SDSS data and the CMB. The effect on BAO measurements for Euclid has yet to be calculated, but the weak lensing effect has been considered for non-canonical UDM models [202]. The change in shape and oscillatory features introduced in the power spectrum allow the sound speed parameter to be constrained very well by Euclid, using 3D weak lensing [427, 506] with errors [see also 198].

Living Rev. Relativity 16, (2013), 6
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