Phase space geometry in scalar-tensor cosmology

TL;DR

This paper analyzes the phase space structure of scalar-tensor cosmological models, revealing a generally two-dimensional curved surface with complex topology, independent of specific coupling functions or potentials in certain cases.

Contribution

It provides a geometric characterization of the phase space in scalar-tensor cosmology, including reduction methods and topological insights.

Findings

Phase space is typically a two-dimensional curved surface.

The topology can be complex with attached sheets.

Results are independent of coupling functions and sometimes potentials.

Abstract

We study the phase space of spatially homogeneous and isotropic cosmology in general scalar-tensor theories. A reduction to a two-dimensional phase space is performed when possible-in these situations the phase space is usually a two-dimensional curved surface embedded in a three-dimensional space and composed of two sheets attached to each other, possibly with complicated topology. The results obtained are independent of the choice of the coupling function of the theory and, in certain situations, also of the potential.