Initial and final de Sitter universes from modified $f(R)$ gravity

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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 non-linear models exhibit multiply de Sitter universe solutions, which often appear in pairs, being one of them 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 dS critical points.