Unified inflation and late-time accelerated expansion with exponential and R2 corrections in modified gravity

Abstract

Modified gravity models with and exponential function of curvature and R2 corrections are proposed. At low curvature, the model explains the matter epoch and the late time accelerated expansion while at the inflation epoch the leading term is R2. At R → 0 the cosmological constant disappears, giving unified description of inflation and dark energy in pure geometrical context. The models satisfy the stability conditions, pass local tests and are viable in the (r, m)-plane, where the trajectories connect the saddle matter dominated critical point (r =-1, m = 0) with the late time de Sitter attractor at r =-2 and 0 < m ≤ 1. Initial conditions were found, showing that the density parameters evolve in a way consistent with current cosmological observations, predicting late time behavior very close to the LCDM with future universe evolving towards the de Sitter attractor.