Viable models of modified gravity which satisfy both local as well as cosmological tests are investigated. It is demonstrated that some versions of such highly nonlinear models exhibit multiple de Sitter universe solutions, which often appear in pairs, one of them being stable and the other unstable. It is explicitly shown that, for some values of the parameters, it is possible to find several de Sitter spaces (as a rule, numerically); one of them may serve for the inflationary stage, while the other can be used for the description of the dark energy epoch. The numerical evolution of the effective equation of state parameter is also presented, showing that these models can be considered as natural candidates for the unification of early-time inflation with late-time acceleration through de Sitter critical points. Moreover, based on the de Sitter solutions, multiple Schwarzschild-de Sitter universes are constructed which might also appear at the (pre-)inflationary stage. Their thermodynamics are studied and free energies are compared.

• Received 28 October 2008

DOI:https://doi.org/10.1103/PhysRevD.79.044001