Possible evolution of a bouncing universe in cosmological models with non-minimally coupled scalar fields

TL;DR

This paper investigates bouncing cosmological models with non-minimally coupled scalar fields, analyzing their dynamics and conditions for bounce solutions, including special cases like conformal coupling and Higgs-like potentials.

Contribution

It introduces new bounce solutions in models with negative coupling constants and polynomial potentials, expanding understanding of non-singular universe evolutions.

Findings

Bounce solutions with non-monotonic Hubble parameters identified

The evolution depends critically on the sign of the cosmological constant

Detailed analysis of conformal coupling and Higgs-like potential cases

Abstract

We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant.