# Effective loop quantum cosmology as a higher-derivative scalar-tensor theory

## TL;DR

This paper demonstrates that a class of higher-derivative scalar-tensor theories, including mimetic gravity, can exactly reproduce the effective dynamics of loop quantum cosmology for various homogeneous and isotropic models.

## Contribution

It establishes a connection between loop quantum cosmology and higher-derivative scalar-tensor theories, extending the correspondence to flat, closed, and open universes.

## Key findings

- Reproduces loop quantum cosmology effective dynamics with scalar-tensor theories.
- Generalizes the result to include different spatial curvatures.
- Identifies a class of mimetic gravity theories matching LQC dynamics.

## Abstract

Recently, Chamseddine and Mukhanov introduced a higher-derivative scalar-tensor theory which leads to a modified Friedmann equation allowing for bouncing solutions. As we note in the present work, this Friedmann equation turns out to reproduce exactly the loop quantum cosmology effective dynamics for a flat isotropic and homogeneous space-time. We generalize this result to obtain a class of scalar-tensor theories, belonging to the family of mimetic gravity, which all reproduce the loop quantum cosmology effective dynamics for flat, closed and open isotropic and homogeneous space-times.