  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 $R + \alpha R^n$ and $R + \alpha R^n
-\delta R^{2-n}$ 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.
