Complete Set of Homogeneous Isotropic Analytic Solutions in Scalar-Tensor Cosmology with Radiation and Curvature

TL;DR

This paper provides an exact, comprehensive set of homogeneous and isotropic solutions in scalar-tensor cosmology with radiation and curvature, revealing cyclic universe behaviors including bounces and antigravity phases, without parameter restrictions.

Contribution

It analytically derives the full set of solutions in scalar-tensor cosmology with radiation and curvature, including special non-generic cases and parameter space analysis.

Findings

Universe undergoes cyclic bounces with antigravity phases.

Existence of non-generic solutions avoiding antigravity entry.

Finite-size bounces occur within a small parameter domain.

Abstract

We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null energy condition. There is a special subset of geodesically complete non-generic solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine tuning initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.