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.
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