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Inflation and dark energy from $f(R)$ gravity

Inflationary paradigm has several issues, such as the pre-inflationary horizon problem or the eternal inflation. To avoid that the standard Starobinsky inflation has been extended to $R + αR^n$ and $R + αR^n -δR^{2-n}$ models as well as Brans-Dicke generalisation of those $f(R)$ models. The region of the parameter space, which provides consistency with PLANCK data and lack of eternal inflation has been founded. The Einstein frame potential has a stable minimum with non-zero vacuum energy, which may be a source of dark energy.