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.

arXiv comment8 pages, Several references added

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Cited by in corpus (6)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• Selected topics in scalar-tensor theories and beyond
• Asymptotic Properties of a Supposedly Regular (Dirac-Born-Infeld) Modification of General Relativity
• Cosmological Perturbation Analysis in a Scale Invariant Model of Gravity
• Notes on Born-Infeld-like modified gravity