Time evolution of the equation of state during perturbative reheating and its impact on the inflationary tensor perturbation spectrum

Abstract: The spectrum of inflationary tensor perturbations is one of the very few available probes of the post-inflationary reheating epoch, and it is strongly influenced by the Universe's equation of state during this period. In the current era of precision cosmology, an accurate estimation of this primordial tensor perturbation spectrum is crucial. Unlike the conventional assumption of a constant equation of state during the perturbative reheating phase, in this work we dynamically calculate the time evolution of the reheating equation of state for different values of the inflaton decay rates including their possible time-dependence in some cases. We further investigate its impact on the spectrum of primordial tensor perturbations, focusing on two different inflationary potentials of the E-model {\alpha}-attractor class, with n=1 and n=3. Using this approach, our results indicate that the inflationary tensor perturbations can be enhanced (or suppressed) by a factor of {\sim} 1.5-3 compared to standard calculations assuming a constant inflaton equation of state. Such a variation arises because the evolution of the comoving horizon differs in the two approaches, causing different comoving momentum modes to re-enter the horizon at different times and undergo distinct evolutions.