We present the first Bayesian constraints on the single field inflationary reheating era obtained from cosmic microwave background (CMB) data. After demonstrating that this epoch can be fully characterized by the so-called reheating parameter, we show that it is constrained by the seven years Wilkinson microwave anisotropies probe (WMAP7) data for all large and small field models. An interesting feature of our approach is that it yields lower bounds on the reheating temperature which can be combined with the upper bounds associated with gravitinos production. For large field models, we find the energy scale of reheating to be higher than those probed at the Large Hadron Collider, ${\rho }_{\mathrm{reh}}^{1/4}>17.3\mathrm{TeV}$ at 95% of the confidence limit. For small field models, we obtain the two-sigma lower limits ${\rho }_{\mathrm{reh}}^{1/4}>890\mathrm{TeV}$ for a mean equation of state during reheating ${\overline{w}}_{\mathrm{reh}}=-0.3$ and ${\rho }_{\mathrm{reh}}^{1/4}>390\mathrm{GeV}$ for ${\overline{w}}_{\mathrm{reh}}=-0.2$. The physical origin of these constraints is pedagogically explained by means of the slow-roll approximation. Finally, when marginalizing over all possible reheating history, the WMAP7 data push massive inflation under pressure ($p<2.2$ at 95% of the confidence limit where $p$ is the power index of the large field potentials) while they slightly favor super-Planckian field expectation values in the small field models.

• Received 5 May 2010

DOI:https://doi.org/10.1103/PhysRevD.82.023511