Bounding $f(R)$ gravity by particle production rate
  Several models of $f(R)$ 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 $f(R)$ cosmological backgrounds. Specifically, we compare the
Bogolubov transformations associated to different vacuum states for some $f(R)$
models. The procedure consists in fixing the $f(R)$ 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 $f(R)$ model. The approach is
developed in both metric and Palatini formalism.
