# Asymptotically Free Mimetic Gravity

## TL;DR

This paper introduces a mimetic gravity model where the gravitational constant diminishes at high curvature, preventing singularities and leading to de Sitter-like solutions, with quantum fluctuations vanishing at the limiting curvature.

## Contribution

It proposes a novel asymptotically free mimetic gravity framework that avoids singularities by making the gravitational constant vanish at a limiting curvature.

## Key findings

- Singularities are avoided in Friedmann and Kasner universes.
- Solutions approach de Sitter space with limiting curvature.
- Quantum metric fluctuations vanish at the limiting curvature.

## Abstract

The idea of "asymptotically free" gravity is implemented using a constrained mimetic scalar field. The effective gravitational constant is assumed to vanish at some limiting curvature. As a result singularities in contracting spatially flat Friedmann and Kasner universes are avoided. The solutions in both cases approach de Sitter metric with a limiting curvature.We show that quantum metric fluctuations vanish when this limiting curvature is approached.