
TL;DR
This paper explores bouncing cosmologies within modified gravity theories based on the Hubble parameter squared, showing how such models can avoid initial singularities and analyzing their stability at linear perturbation levels.
Contribution
It demonstrates that simple Lagrangians depending on Hubble squared can produce bouncing solutions and analyzes their phase space and stability properties.
Findings
Bouncing solutions are obtained when phase space curves are closed and cross H=0 twice.
The simplest example is the ellipse in the holonomy corrected Friedmann equation in Loop Quantum Cosmology.
Linear perturbations do not exhibit Ostrogradski instability, but it may appear at higher orders.
Abstract
The theory of inflation is one of the fundamental and revolutionary developments of modern cosmology that became able to explain many issues of early universe in the context of the standard cosmological model (SCM). However, the initial singularity of the universe, where physics is indefinite, is still obscure in the combined `SCM+inflation' scenario. An alternative to `SCM+inflation' without the initial singularity is thus always welcome, and bouncing cosmology is an attempt of that. The current work is thus motivated to investigate the bouncing solutions in modified gravity theories when the background universe is described by the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. We show that the simplest way to obtain the bouncing cosmologies in such spacetime is to consider some kind of Lagrangians whose gravitational sector depends only on the square of the Hubble…
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