Stable, Accelerating Universes in Modified Gravity

TL;DR

This paper demonstrates that certain modified gravity theories, specifically $f(R)=R\u00b1\u03bc^4/R$, can produce a stable, accelerating universe without dark energy, while remaining consistent with solar system tests.

Contribution

It introduces a perturbative approach to $f(R)$ gravity that avoids instabilities and matches observational constraints, showing these models can explain cosmic acceleration.

Findings

The $f(R)=R\u00b1\u03bc^4/R$ model yields a flat, accelerating universe.

The model is consistent with solar system PPN measurements.

It does not require dark energy to produce acceleration.

Abstract

Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have been studied in great detail. When considered as complete theories of gravity they can generate non-perturbative deviations from the general relativistic predictions in the solar system, and the simplest models show instabilites on cosmological scales. Here we show that it is possible to treat $f(R)=R\pm\mu^4/R$ gravity in a perturbative fashion such that it shows no instabilities on cosmological scales and, in the solar system, is consistent with measurements of the PPN parameters. We show that such a theory produces a spatially flat, accelerating universe, even in the absence of dark energy and when the matter density is too small to close the universe in the general relativistic case.