Dark Energy and Equation of State Oscillations with Collisional Matter
  Fluid in Exponential Modified Gravity
  We study some aspects of cosmological evolution in a universe described by a
viable curvature corrected exponential $F(R)$ gravity model, in the presence of
matter fluids consisting of collisional matter and radiation. Particularly, we
express the Friedmann-Robertson-Walker equations of motion in terms of
parameters that are appropriate for describing the dark energy oscillations and
compare the dark energy density and the dark energy equation of state parameter
corresponding to collisional and non-collisional matter. In addition to these,
and owing to the fact that the cosmological evolution of collisional and
non-collisional matter universes, when quantified in terms of the Hubble
parameter and the effective equation of states parameters, is very much alike,
we further scrutinize the cosmological evolution study by extending the
analysis to the study of matter perturbations in the matter domination era. We
quantify this analysis in terms of the growth factor of matter perturbations,
in which case the resulting picture of the cosmological evolution is clear,
since collisional and non-collisional universes can be clearly distinguished.
Interestingly enough, since it is known that the oscillations of the effective
equation of state parameter around the phantom divide are undesirable and
unwanted in $F(R)$ gravities, when these are considered for redshifts near the
matter domination era and before, in the curvature corrected exponential model
with collisional matter which we study here there exist oscillations that never
cross the phantom divide. Therefore, this rather unwanted feature of the
effective equation of state parameter is also absent in the collisional matter
filled universe.
