Bouncing Cosmological Isotropic Solutions in Scalar-Tensor Gravity

TL;DR

This paper explores new bouncing, non-singular isotropic cosmological solutions within scalar-tensor gravity, highlighting conditions for their existence and stability, especially with bounded Higgs-like potentials, and analyzing their properties using an effective potential approach.

Contribution

It introduces new families of bouncing solutions in scalar-tensor gravity with bounded potentials, contrasting previous unbounded potential models, and analyzes their stability and properties.

Findings

Bouncing solutions exist with Higgs-like potentials bounded from below.

Some solutions are regular but unstable under perturbations.

Regular solutions require specific conditions on the effective potential's maximum.

Abstract

Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzed using an effective potential as the main tool. Bouncing solutions are shown to exist for a Higgs-like self-interaction potential which is bounded from below, in contrast to previous solutions that appeared in the literature based on potentials which were unbounded from below. In the simplest version of a scalar field with the quartic potential and conformal coupling to gravity, bouncing spatially flat solutions either have the Hubble function diverging in the past before the bounce, but with a well-behaved future, or are globally regular but unstable with respect to anisotropic or inhomogeneous perturbations at some finite values of the scalar field and curvature. Regular solutions can only exist in the part of the parameter space where the maximum of the effective potential is larger than the first zero of the potential, and gravity becomes repulsive at the bounce.