Some Late-time Asymptotics of General Scalar-Tensor Cosmologies

TL;DR

This paper analyzes the late-time behavior of scalar-tensor cosmologies, identifying conditions on the coupling function for the universe to approach de Sitter space and discussing implications for the variation of the gravitational constant.

Contribution

It provides new criteria on the scalar-tensor coupling function for asymptotic de Sitter expansion and classifies late-time variations of the gravitational constant in these theories.

Findings

Conditions on omega(phi) for de Sitter approach

Classification of G(t) variations at late times

Scalar-tensor theories can avoid Boltzmann brain problem

Abstract

We study the asymptotic behaviour of isotropic and homogeneous universes in general scalar-tensor gravity theories containing a p=-rho vacuum fluid stress and other sub-dominant matter stresses. It is shown that in order for there to be approach to a de Sitter spacetime at large 4-volumes the coupling function, omega(phi), which defines the scalar-tensor theory, must diverge faster than |phi_infty-phi|^(-1+epsilon) for all epsilon>0 as phi rightarrow phi_infty <> 0 for large values of the time. Thus, for a given theory, specified by omega(phi), there must exist some phi_infty in (0,infty) such that omega -> infty and omega' / omega^(2+epsilon) -> 0 as phi -> 0 phi_infty in order for cosmological solutions of the theory to approach de Sitter expansion at late times. We also classify the possible asymptotic time variations of the gravitation `constant' G(t) at late times in scalar-tensor theories. We show that (unlike in general relativity) the problem of a profusion of ``Boltzmann brains'' at late cosmological times can be avoided in scalar-tensor theories, including Brans-Dicke theory, in which phi -> infty and omega ~ o(\phi^(1/2)) at asymptotically late times.