Note on stability of de Sitter solutions of f(R) theories

The consequences of the constraints which stability of de Sitter solutions 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 matching of local solutions with background de Sitter spaces. Otherwise, asymptotic matching of local solutions of the corresponding models with maximally symmetric spaces of constant curvature is either unstable or anti-de Sitter space is the only stable asymptotic solution. Additional arguments are given in favor 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 in which 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 literature.