Accounting for the time evolution of the equation of state parameter
  during reheating
  One of the important parameters in cosmology is the parameter characterizing
the equation of state (EoS) of the sources driving the cosmic expansion. Epochs
that are dominated by radiation, matter, or scalar fields, whether they are
probed either directly or indirectly, can be characterised by a unique value of
this parameter. However, the EoS parameter during reheating---a phase
succeeding inflation which is supposed to rapidly defrost our
universe---remains to be understood satisfactorily. In order to circumvent the
complexity of defining an instantaneous EoS parameter during reheating, an
effective parameter $w_\mathrm{eff}$, which is an average of the EoS parameter
over the duration of reheating, is usually considered. The value of
$w_\mathrm{eff}$ is often chosen arbitrarily to lie in the range $-1/3 \leq
w_\mathrm{eff} \leq 1$. In this work, we consider the time evolution of the EoS
parameter during reheating and relate it to inflationary potentials $V(\phi)$
that behave as $\phi^p$ around the minimum, a proposal which can be applied to
a wide class of inflationary models. We find that, given the index $p$, the
effective EoS parameter $w_{\rm eff}$ is determined uniquely. We discuss the
corresponding effects on the reheating temperature and its implications.
