Bounding f(R) gravity by particle production rate

Abstract

Several models of [Formula: see text] gravity have been proposed in order to address the dark side problem in cosmology. However, these models should be constrained also at ultraviolet scales in order to achieve some correct fundamental interpretation. Here, we analyze this possibility comparing quantum vacuum states in given [Formula: see text] cosmological backgrounds. Specifically, we compare the Bogolubov transformations associated to different vacuum states for some [Formula: see text] models. The procedure consists in fixing the [Formula: see text] free parameters by requiring that the Bogolubov coefficients can be correspondingly minimized to be in agreement with both high redshift observations and quantum field theory predictions. In such a way, the particle production is related to the value of the Hubble parameter and then to the given [Formula: see text] model. The approach is developed in both metric and Palatini formalism.