  Universe history in $R^2$-gravity is studied from "beginning" up to the
present epoch. It is assumed that initially the curvature scalar $R$ was
sufficiently large to induce the proper duration of inflation. Gravitational
particle production by the oscillating $R(t)$ led to a graceful exit from
inflation, but the cosmological evolution in the early universe was drastically
different from the standard one till the universe age reached the value of the
order of the inverse decay rate of the oscillating curvature $R(t)$. This
deviation from the standard cosmology might have a noticeable impact on the
formation of primordial black holes and baryogenesis. At later time, after
exponential decay of the curvature oscillations, cosmology may return to
normality.
