Imperfect Dark Matter

Abstract

We consider cosmology of the recently introduced mimetic matter with higher derivatives (HD). Without HD this system describes irrotational dust—Dark Matter (DM) as we see it on cosmologically large scales. DM particles correspond to the shift-charges—Noether charges of the shifts in the field space. Higher derivative corrections usually describe a deviation from the thermodynamical equilibrium in the relativistic hydrodynamics. Thus we show that mimetic matter with HD corresponds to an imperfect DM which: i) renormalises the Newton's constant in the Friedmann equations, ii) has zero pressure when there is no extra matter in the universe, iii) survives the inflationary expansion which puts the system on a dynamical attractor with a vanishing shift-charge, iv) perfectly tracks any external matter on this attractor, v) can become the main (and possibly the only) source of DM, provided the shift-symmetry in the HD terms is broken during some small time interval in the radiation domination époque.In the second part of the paper we present a hydrodynamical description of general anisotropic and inhomogeneous configurations of the system. This imperfect mimetic fluid has an energy flow in the field's rest frame. We find that in the Eckart and in the Landau-Lifshitz frames the mimetic fluid possesses nonvanishing vorticity appearing already at the first order in the HD. Thus, the structure formation and gravitational collapse should proceed in a rather different fashion from the simple irrotational DM models.

Initial conditions for imperfect dark matter

“…In the situation with the zeroth Noether charge, IDM tracks the total matter filling in the Universe [3]. Indeed, the physical energy density is related to the Noether charge density by…”

“…This allows to generate nonzero Noether charge, which, by the suitable choice of parameters, can be tuned to match the observed value [3]. With no much loss of generality, we consider an instantaneous transition from some initial value γ 1 to the value γ 2 > γ 1 .…”

“…In the present paper, we continue to discuss Imperfect Dark Matter (IDM) scenario [2,3] (Modified Dust in Ref. [2]).…”

“…In this situation, the model possesses shift symmetry ϕ → ϕ + c. There is, consequently, the Noether charge density that redshifts away as the inverse third power of the scale factor. Up to the term suppressed by the γ factor, the energy density of IDM is equal to the Noether charge density [3] (Section 2). Hence, with a good accuracy, the cosmological evolution of IDM mimics that of the dust particles 2 .…”

“…The reason is that the Noether charge density gets washed out during inflation with an exponential accuracy. In this situation, IDM constitutes only a tiny, O(γ), fraction of the overall DM during the dust dominated stage [3]. To avoid this, one necessarily assumes breaking of the shift symmetry taking place at the early stages of the Universe, i.e., deeply in the radiation dominated (RD) era.…”