# Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity

## TL;DR

This paper develops a reconstruction method for mimetic gravity tailored to bouncing cosmologies, connecting it with quantum gravity models like loop quantum cosmology and group field theory, and analyzing stability and anisotropies.

## Contribution

It introduces a general reconstruction procedure for mimetic gravity in bouncing universes, linking it with quantum gravity models and exploring stability and anisotropy evolution.

## Key findings

- Reconstruction of mimetic gravity functions from quantum gravity models.
- Analysis of anisotropy behavior near the bounce.
- Discussion of scalar perturbation stability.

## 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 $f(\Box\phi)$ 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.