Stable, Accelerating Universes in Modified Gravity

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.

5 pages, 1 figure, matches published version

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Cited by in corpus (3)

• Gödel-type universes in f(R) gravity
• Covariant Effective Action for Loop Quantum Cosmology from Order Reduction
• Gravity with Perturbative Constraints: Dark Energy Without New Degrees of Freedom