S. H. Pereira, J. C. Z. Aguilar, E. C. Romão
In this paper we present an alternative mechanism to generate dark matter particles throughout the decay of virtual scalar massless particles into real particle-antiparticle pairs. In order to illustrate such mechanism, we discuss quantitatively the problem of massless particle creation in a flat, homogeneous and isotropic universe expanding with a scale factor proportional to $t^{8/3}$, which follows directly from a particular $f(R)$ theory of gravity. We find that the spectrum of the total number and total energy of created particles can be determined exactly for any value of the physical time in a matter dominated universe. We also 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. In the absent of an appropriated energy scale, 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 $10^3$ times the present critical energy density. By applying the method of space-time correlation function we conclude that such particles are virtual ones, forming a background field similar to the cosmic microwave background radiation. This opens the possibility that the decay of these virtual particles into massive particle-antiparticle pairs could be an alternative mechanism to generate particles of dark matter throughout the universe evolution. Moreover, this theory is naturally accelerated, giving an explanation for the current phase of acceleration of the universe.
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http://arxiv.org/abs/1108.3346
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