Modified gravity with an exponential function of curvature

Abstract

The role of an exponential function of the scalar curvature in the modified gravity is analyzed. Two models are proposed. A toy model that complies with local and cosmological constraints and gives appropriate qualitative description of the cosmic evolution. This model contains a saddle matter-dominant critical point that can evolve towards a late time de Sitter attractor. Initial conditions have been proposed, showing that this toy model has an acceptable matter era and gives an approximate qualitative behavior of cosmic evolution. A second viable model, behaves very close to Λ CDM at early times and can satisfy local and cosmological constraints. It behaves as R- 2 Λ at R→ ∞ and tends to zero at R→ 0 , containing flat spacetime solution. The model gives viable cosmological trajectories that, as the first model, connect the matter dominated point with a late time de Sitter attractor. The cosmic evolution of the main density parameters in this model is consistent with current observations with an equation of state very close to - 1.