Reconstructing f(R) Gravity from a Chaplygin Scalar Field in de Sitter Spacetimes

Abstract

We present a reconstruction technique for models of $f(R)$ gravity from the Chaplygin scalar field in flat de Sitter spacetimes. Exploiting the equivalence between $f(R)$ gravity and scalar-tensor theories, and treating the Chaplygin gas as a scalar field model in a universe without conventional matter forms, the Lagrangian densities for the $f(R)$ action are derived. Exact $f(R)$ models and corresponding scalar field potentials are obtained for asymptotically de Sitter spacetimes in early and late cosmological expansion histories. It is shown that the reconstructed $f(R)$ models all have General Relativity as a limiting solution.

20 pages, 10 figures

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• The Chaplygin gas as a model for modified teleparallel gravity?
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
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• Perturbations of quasi-Newtonian universes in scalar-tensor gravity
• Inflationary f(R) cosmologies