It is shown that F (R)-modified gravitational theories lead to curvature oscillations in astrophysical systems with rising energy density. The frequency and the amplitude of such oscillations could be very high and would lead to noticeable production of energetic cosmic ray particles.There are two popular phenomenological explanations of the observed accelerated universe expansion. It is either prescribed to the existence of the so called dark energy (DE) with the equation of statewhere P and ρ are respectively pressure and energy densities. Another way to describe cosmological acceleration is a modification of the classical action of general relativity (GR) by an addition of a non-linear function of curvature, F (R):where the function F (R) is chosen in such a way that the modified GR equations have a solution R = const in absence of any matter source. Taking the trace g μν δA/δg μν = 0, we findwhere D 2 ≡ D μ D μ is the covariant D'Alambertian operator, F R ≡ dF /dR, and T μν is the energy-momentum tensor of matter.a

The universe evolution during the radiation-dominated epoch in the R 2 -extended gravity theory is considered. The equations of motion for R and H are solved analytically and numerically. The particle production rate by the oscillating curvature is calculated in one-loop approximation and the back-reaction of particle production on the evolution of R is taken into account. Possible implications of the model for cosmological creation of non-thermal dark matter is discussed.

We study particle production in infrared-modified gravitational theories in the contemporary universe. It is shown that in astronomical systems with rising mass density, the curvature scalar may oscillate with very high frequency. These oscillations lead to efficient particle production and in an interesting range of model parameters could be a source of energetic cosmic rays. This effect either excludes some models of modified gravity or suggests a new mechanism of cosmic ray production.