Scalar-Tensor Cosmologies and their Late Time Evolution

TL;DR

This paper investigates the late-time evolution of scalar-tensor cosmological models, showing how scalar fields influence the universe's approach to general relativity or other final states, depending on the scalar potential and universe geometry.

Contribution

It generalizes previous results by analyzing open universes and self-interacting scalar fields, revealing conditions under which the universe approaches general relativity or retains scalar effects.

Findings

Open universe scalar fields tend to reduce scalar contribution but may not fully reach general relativity.

Self-interacting scalar potentials dominate late-time behavior, often leading to negligible scalar effects.

The attractor mechanism's effectiveness depends on the scalar potential and universe geometry.

Abstract

We study the asymptotic behavior at late times of Friedmann-Robertson-Walker (uniform density) cosmological models within scalar-tensor theories of gravity. Particularly, we analyze the late time behavior in the present (matter dominated) epoch of the universe. The result of Damour and Nordtvedt that for a massless scalar in a flat cosmology the Universe evolves towards a state indistinguishable from general relativity is generalized. We first study a massless scalar field in an open universe. It is found that, while the universe tends to approach a state with less scalar contribution to gravity, the attractor mechanism is not effective enough to drive the theory towards a final state indistinguishable from general relativity. For the self-interacting case it is found that the scalar field potential dominates the late time behavior. In most cases this makes the attractor mechanism effective, thus resulting in a theory of gravity with vanishingly small scalar contribution even for the open Universe.