Evolution and heating of the universe in $R^2$-modified gravity are considered. It is shown that the universe’s history can be separated into four different epochs: (1) inflation, (2) heating due to curvature oscillations (scalaron decay), (3) transition to matter dominated period, and (4) conventional cosmology governed by General Relativity. Cosmological density of dark matter (DM) particles for different decay channels of the scalaron is calculated. The bounds on the masses of DM particles are derived for the following dominant decay modes: to minimally coupled scalars, to massive fermions, and to gauge bosons.

Universe history in R²-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.

Cosmological evolution and particle creation in \(R^2\)-modified gravity are considered for the case of the dominant decay of the scalaron into a pair of gauge bosons due to conformal anomaly. It is shown that in the process of thermalization superheavy dark matter with the coupling strength typical for the GUT SUSY can be created. Such dark matter would have the proper cosmological density if the particle mass is close to \(10^{12}\) GeV.

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.

Cosmological evolution and particle creation in $R^2$-modified gravity are considered for the case of the dominant decay of the scalaron into a pair of gauge bosons due to conformal anomaly. It is shown that in the process of thermalization superheavy dark matter with the coupling strength typical for the GUT SUSY can be created. Such dark matter would have the proper cosmological density if the particle mass is close to $10^{12}$ GeV.