Reconstruction of Mimetic Gravity in a Non-Singular Bouncing Universe from Quantum Gravity

Abstract

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function f ( φ) implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power law expansions of f in different regimes, corresponding e.g. to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we discuss two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational "constants" in the cosmological equations.

Theories with limited extrinsic curvature and a nonsingular anisotropic universe

“…It is straightforward to see that the equations of motion for the cuscuton-type model coincide with those for the mimetic-type model if we replace A μ with −∇ μ ϕ, except for the appearance of u μ in (24). As shown in (23), this u μ is nothing but an integration constant originating from the covariant derivative in (22c) for the mimetic case.…”

“…As an example, current models of limiting curvature mimetic gravity exactly yield the cosmological background equations of LQC (see, e.g., Refs. [19][20][21][22][23][24][25][26], as well as Refs. [27][28][29][30] in other quantum gravity contexts).…”

“…We use the covariant equations of motion (22a), (22b), and (24) to study the spacetime dynamics. 8 In what follows, we choose the N ¼ 1 gauge.…”

“…In what follows, we choose the plus branch of (30a) so that ϕ behaves as our clock. The evolution of the Hubble parameter and the anisotropies is determined from the modified Einstein equation (24). The anisotropies σ AE ¼ _ β AE can be obtained as…”

A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories

“…In the presence of matter with a generic equation of state, solving the effective Friedmann equation (48) is a more challenging task. Nonetheless, it remains possible to integrate the equations around the bounce [43]; and then the time-dependent quasi-Kasner exponents are readily computed.…”