The origin of ultra-high-energy cosmic rays, with energies around the GZK (Greisen-Zatsepin-Kuzmin) cut-off, remains an unsolved mystery. According to this cut-off, the mean free path of very energetic particles in the Universe does not exceed 50 megaparsec, due to their scattering on the cosmic microwave background radiation. However, there are no conventional sources of ultra-high-energy cosmic rays inside this radius. Hence some new sources seem to be necessary.

In the present letter a novel and intriguing explanation is suggested that links far-reaching fundamental aspects of F(R) modified theories to an efficient production of highly energetic cosmic rays during the recent history of the Universe (let us recall that F(R) theories present a modification of the usual General Relativity by an addition of a non-linear function F(R) of the scalar curvature R. This function is chosen in such a way that it leads to accelerated cosmological expansion indicated by the recent astronomical data).

At the core of this work lies the proof that in cosmological and astrophysical systems with rising energy densities, the F(R) modified theories of gravity exhibit powerful oscillations of the curvature scalar R, with an amplitude much larger than the standard value of curvature predicted by the General Relativity. These oscillations are strongly anharmonic, with frequencies that can be as large as billions of GeV. This striking and rather unexpected oscillatory behaviour of R lends support to the idea that ultra-high energy cosmic rays can be generated by such curvature oscillations at the appropriate cosmological redshifts.