No cosmic rays from curvature oscillations during structure formation in $F(R)$ gravity

The Starobinsky model of modified gravity suggested to explain dark energy may also be considered in the astrophysical context. Recently it has been pointed out that in contracting regions curvature oscillations around the general relativity (GR) value may lead to the production of high energy particles that contribute to the cosmic ray flux. We revisit these calculations in the Einstein frame and show that the continuous approximation for the matter density used in the original calculations is not valid. We show that this problem is generic in $F(R)$-gravity models introduced to describe the dark energy. We go beyond the approximation and find the rate of particle production to be negligible.

Figure 1

These plots show the evolution of $\xi -{\xi }_{\min }$ for $\kappa =0.08$ (left), $\kappa =0.03$ (middle), and $\kappa =0.01$ (right). The blue line corresponds to initial conditions $\xi ({\tau }_0)={\xi }_{\min }({\tau }_0)$, ${\xi }^{\prime }({\tau }_0)={\xi }_{\min }^{\prime }({\tau }_0)$ imposed at ${\tau }_0=-1.5/\kappa$, and the violet line is for ${\tau }_0=0$. Taking the earlier initial time for the first choice of conditions provides the same result.