Stability of cosmological singularity-free solutions in quadratic gravity

TL;DR

This paper presents a family of homogeneous, isotropic, singularity-free cosmological solutions in quadratic gravity, analyzes their stability, and discusses their potential to replace the Big Bang singularity with a smooth origin.

Contribution

It introduces and analyzes a new class of singularity-free cosmological solutions in quadratic gravity, highlighting their unstable nature and dependence on model parameters.

Findings

Solutions are singularity-free at early and late times.

Stability analysis shows these solutions are generally unstable.

A Big Bang can emerge from a non-singular regime with parameter adjustments.

Abstract

We introduce a large family of homogeneous and isotropic cosmological solutions in quadratic gravity which are singularity-free at early and late times. This kind of smooth solutions only emerges beyond the unstable de Sitter branch $3\alpha < \beta$, $\alpha$ being the coupling of the $R^2$ term and $-\beta$ the coupling of the $R_{\mu\nu}^2$ term. We have analyzed the stability of these singularity-free solutions by computing the second-order variation of the action. The complete analysis shows that a Big Bang can emerge from a singularity-free regime when the parameters of the theory are slightly modified, revealing the unstable nature of this type of solutions.