Higher Powers in Gravitation

TL;DR

This paper analyzes the asymptotic behavior of generalized f(R) gravity cosmologies, revealing that the dominance of higher or lower powers of R varies over time and challenges previous assumptions about early and late universe dynamics.

Contribution

It provides a comprehensive analysis of the asymptotic behavior of f(R) cosmologies, showing that the highest or lowest powers of R do not always dominate as previously assumed.

Findings

Higher powers of R can dominate late-time behavior.

Lower powers of R often dominate at early times.

Behavior varies with different solutions and matter contents.

Abstract

We consider the Friedmann-Robertson-Walker cosmologies of theories of gravity that generalise the Einstein-Hilbert action by replacing the Ricci scalar, R, with some function, f(R). The general asymptotic behaviour of these cosmologies is found, at both early and late times, and the effects of adding higher and lower powers of R to the Einstein-Hilbert action is investigated. The assumption that the highest powers of R should dominate the Universe's early history, and that the lowest powers should dominate its future is found to be inaccurate. The behaviour of the general solution is complicated, and while it can be the case that single powers of R dominate the dynamics at late times, it can be either the higher or lower powers that do so. It is also shown that it is often the lowest powers of R that dominate at early times, when approach to a bounce or a Tolman solution are generic possibilities. Various examples are considered, and both vacuum and perfect fluid solutions investigated.