Reheating temperature from the CMB

TL;DR

This paper develops a method to constrain the reheating temperature after inflation using CMB data, deriving an expression independent of certain unknowns, and estimates the reheating temperature as approximately 3.5 million GeV.

Contribution

It extends previous methods to derive a reheating temperature constraint that is independent of the relativistic degrees of freedom, using WMAP 7 data.

Findings

Reheating temperature estimated at 3.5 x 10^6 GeV.

Derived an expression for reheating temperature independent of g_*.

Uncertainty in the estimate is about 53%, expected to decrease with future data.

Abstract

In the recent paper by Mielczarek \emph{et al.} (JCAP {\bf 1007} (2010) 004) an idea of the method which can be used to put some constraint for the reheating phase was proposed. Another method of constraining the reheating temperature has been recently studied by Martin and Ringeval (Phys.\ Rev.\ D {\bf 82} (2010) 023511). Both methods are based on observations of the cosmic microwave background (CMB) radiation. In this paper, we develop the idea introduced in this first article to put constraint on the reheating after the slow-roll inflation. We restrict our considerations to the case of a massive inflaton field. The method can be, however, easily extended to the different inflationary scenarios. As a main result, we derive an expression on the reheating temperature $T_{\text{RH}}$. Surprisingly, the obtained equation is independent on the unknown number of relativistic degrees of freedom $g_*$ produced during the reheating. Based on this equation and the WMAP 7 observations, we find $T_{\text{RH}}=3.5\cdot 10^6$ GeV, which is consistent with the current constraints. The relative uncertainty of the result is, however, very high and equal to $\sigma(T_{\text{RH}})/T_{\text{RH}} \approx 53$. As we show, this uncertainty will be significantly reduced with future CMB experiments.