A Note on de Sitter Embedding of $f(R)$ Theories

Abstract

The consequences of the constraints which de Sitter embedding of $f(R)$ theories imposes on the Lagrangian's parameters, are investigated within the metric formalism. It is shown, in particular, that several common $f(R)$ Lagrangians do not actually admit such an embedding. Otherwise, asymptotic matching of local solutions of the corresponding models with background (maximally symmetric) spaces of constant curvature is either unstable or, anti-de Sitter embedding is the only stable embedding. Additional arguments are given in favour of a previous claim that a class of $f(R)$ models comprising both positive and negative powers of $R$ (two different mass scales), could be a nice scenario where to address, in a united picture, both early-time inflation and late-time accelerated expansion of the universe. The approach undertaken here is used, also, to check ghost-freedom of a Dirac-Born-Infeld modification of general relativity previously studied in the bibliography.

8 pages, Several references added

References in corpus (13)

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• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
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• Are f(R) dark energy models cosmologically viable ?
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Cited by in corpus (3)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Selected topics in scalar-tensor theories and beyond
• Asymptotic Properties of a Supposedly Regular (Dirac-Born-Infeld) Modification of General Relativity