Reconstructing f(R) gravity from a Chaplygin scalar field in de Sitter spacetimes

Abstract

We present a reconstruction technique for models of [Formula: see text] gravity from the Chaplygin scalar field in flat de Sitter spacetimes. Exploiting the equivalence between [Formula: see text] gravity and scalar–tensor (ST) theories, and treating the Chaplygin gas (CG) as a scalar field model in a universe without conventional matter forms, the Lagrangian densities for the [Formula: see text] action are derived. Exact [Formula: see text] 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 [Formula: see text] models all have General Relativity (GR) as a limiting solution.