Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity

Abstract

Recently modified gravitational theories which mimic the behaviour of dark matter, the so-called "Mimetic Dark Matter", have been proposed. We study the consistency of such theories with respect to the absence of ghost instability and propose a new tensor-vector-scalar theory of gravity, which is a generalization of the previous models of mimetic dark matter with additional desirable features. The original model proposed by Chamseddine and Mukhanov [JHEP 11 (2013) 135] is concluded to describe a regular pressureless dust, presuming that we consider only those configurations where the energy density of the mimetic dust remains positive under time evolution. For certain type of configurations the theory can become unstable. Both alternative modified theories of gravity, which are based on a vector field (tensor-vector theory) or a vector field and a scalar field (tensor-vector-scalar theory), are free of ghost instabilities.

Derivative-dependent metric transformation and physical degrees of freedom

“…The mimetic limit is achieved when χ becomes a conformal gauge degree of freedom and can be set to unity, thus recovering the results in the literature [41,43,45], where one has the original action plus a constraint given by…”

“…Moreover when the transformation between two theories is singular, whether one of the theories can be a consistent truncation of the other is also an interesting question. In particular for the case of the original theory of Chamseddine and Mukhanov [38,39], the Hamiltonian analysis yields that the physical degrees of freedom in fact increase in number [42,43]. However, in the original mimetic gravity the scalar field is non-dynamical, i.e.…”

“…However, in the original mimetic gravity the scalar field is non-dynamical, i.e. there is no kinetic term, and the singular transformation leads to a new conformal gauge degree of freedom [43], a.k.a. the mimetic degree of freedom.…”

“…In that sense, as shown in Sec. IV and inspired in the alternative formulation of mimetic gravity [41,43,45], one might expect that by treating the seemingly problematic X dependence as a new field, say χ, introduced by a Lagrange multiplier λ, namely…”

Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry

“…To resolve conformal symmetry and to be ghost-free, a model recently proposed as titled Mimetic F (R) gravity [43]. It is inspired from the mimetic theory [34,35,36,37,39,40,42], a model in which dark matter problem is resolved as an integration constant. Also, it is self consistent with conformal symmetry.…”