### Quo vadis dark matter theoretical research ?

**The stuff some dreams of quantum gravity are made of ...**

The origin of Dark Matter (DM) is one of the oldest and biggest puzzles in cosmology and particle physics. Surprisingly, even basic macroscopic nature of DM is not yet understood–indeed, we do not know whether DM is a gas of some particles beyond the Standard Model (SM){... composed from the so-called Weakly Interacting Massive Particles (WIMPs) [1], sterile right-handed neutrinos [2] and even different and some times numerous copies of the SM, see e.g. [3, 4] just to mention few options. Whether the axion DM [5, 6] represents a condensate or not is still debated, for the most recent discussion see [7]. DM can also be}a gas of primordial black holes see e.g. [8, 9], or some other macroscopic objects, see e.g. [10], or some ﬂuid e.g. [11] or Bose-Einstein condensates – some classical scalar ﬁelds e.g. [12], [13, 14] or even some effective solid [15]. In the latter approach where one assumes high occupation numbers of some new ﬁelds, we can also incorporate the relativistic version of MOND [16] - TeVeS [17] and numerous others modiﬁcations of general relativity (GR), e.g. [18]. The simplest modiﬁcation of GR can be achieved by promoting it to a scalar-tensor theory.

GR enjoys a very powerful symmetry – diffeomorphism invariance.One of the manifestations of its power is that one can parametrize the metric gµν by a scalar ﬁeld ϕ and an auxiliary metric lµν in a general disformal way[19]

g_{µν}= C(ϕ,X)l_{µν}+D(ϕ,X)ϕ,_{µ}ϕ,_{ν}(1.1)

where X = 1/2*l^{µν}ϕ,_{µ}ϕ,_{ν}and C(ϕ,X) and D(ϕ,X) are free functions, and obtain the Einstein equations (for gµν) by variation of the action with respect to ϕ and lµν instead of gµν, see [25].The only exception from this rule corresponds to a singular parameterisation when[25]

D(ϕ,X)= f (ϕ)− C(ϕ,X)/2X . (1.2)

When the transformation is singular, there are new degrees of freedom and new physics modifying GR.Mimetic Dark Matter[26] is one of the theories of this type and makes use of the transformation (1.1) with C =2X and D =0.It is important that in this case the system is Weyl invariant with respect to the transformations of the auxiliary metricl_{µν}. Soon it was realised thatMimetic Dark Matter is equivalent to the ﬂuid description of irrotational dust [27, 28] with the mimetic ﬁeld ϕ playing the role of the velocity potential. Models of this type also appear in the IR limit of the projectable version of Hořava-Lifshitz gravity [29, 30, 31] and correspond to a scalar version of the so-called Einstein Aether [32].Surprisingly these models can also emerge in the non-commutative geometry [33]. In [34] this class of systems was further extended by i) adding a potential V(ϕ) which allows to obtain an arbitrary equation of state for this dust-like matter with zero sound speed, as it was done earlier in [35]; ii) by introducing the higher derivatives (HD) which provide a nonvanishing sound speed. The latter modiﬁcation allowed one to study inﬂationary models with the creation of quantum cosmological perturbations. Moreover, this ﬁnite sound speed can suppress the structure on small scales [36] and have other interesting phenomenological consequences.

(Submitted on 22 Dec 2014)

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