Reheating temperature from the CMB
  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.
