Abstract
In this paper we present an alternative mechanism to generate dark matter particles. We discuss quantitatively the problem of massless particle creation in a flat, homogeneous and isotropic universe expanding with a scale factor which follows directly from a particular f (R) theory of gravity. We find that the main contribution to the total number of particles and total energy comes from small wavenumbers k and particles with large values of k are produced only in the future. If we choose the minimal mode k as corresponding to the maximum wavelength inside the Hubble horizon, we can estimate the present energy density of such massless particles as 10^{-120} times the present critical energy density. Such particles form a background field similar to the cosmic microwave background radiation, which could be interpreted as dark matter particles. The study presented here might be the basis for future researches related to the creation of matter in the universe for various models of evolution.
