Bouncing cosmologies via modified gravity in the ADM formalism: Application to Loop Quantum Cosmology

TL;DR

This paper explores how modified gravity theories within the ADM formalism can naturally produce bouncing cosmologies, including those inspired by Loop Quantum Cosmology, and aims to develop gauge-invariant perturbation equations for these models.

Contribution

It introduces a covariant framework for bouncing cosmologies using multivalued $f$ functions in the ADM formalism, linking to Loop Quantum Cosmology and deriving gauge-invariant perturbation equations.

Findings

Bouncing solutions emerge naturally from multivalued $f$ functions.

The approach reproduces features of Loop Quantum Cosmology.

Gauge-invariant perturbation equations are formulated for matter bounce scenarios.

Abstract

We consider the ADM formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond General Relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the universe following the spirit of Weyl's postulate, has been fixed, $f$ theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation, i.e., the constraint and dynamical equations have the same form for all these observers. Moreover, choosing multivalued $f$ functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected Loop Quantum Cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.