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 $f(\square \varphi )$ 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.

Invited article for the special issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms" of the journal "Universe"; 21 pages, 2 figures; v2: matches published version

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• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• Theories with limited extrinsic curvature and a nonsingular anisotropic universe
• Climbing over the potential barrier during inflation via null energy condition violation
• Editorial for the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms"
• Arrows of time in bouncing cosmologies