Equation-of-state parameter for reheating

Abstract

Constraints to the parameters of inflation models are often derived assuming some plausible range for the number--e.g., $N_k=46$ to $N_k=60$--of $e$-folds of inflation that occurred between the time that our current observable Universe exited the horizon and the end of inflation. However, that number is, for any specific inflaton potential, related to an effective equation-of-state parameter $w_{\mathrm{re}}$ and temperature $T_{\mathrm{re}}$, for reheating. Although the physics of reheating is highly uncertain, there is a finite range of reasonable values for $w_{\mathrm{re}}$. Here we show that by restricting $w_{\mathrm{re}}$ to this range, more stringent constraints to inflation-model parameters can be derived than those obtained from the usual procedure. To do so, we focus in this work in particular on natural inflation and inflation with a Higgs-like potential, and on power law models as limiting cases of those. As one example, we show that the lower limit to the tensor-to-scalar ratio $r$, derived from current measurements of the scalar spectral index, is about 20%-25% higher (depending on the model) with this procedure than with the usual approach.