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 TeV at 95 \% of confidence .
For small field models , we obtain the two-sigma lower limits \rho _ { \mathrm { reh } } ^ { 1 / 4 } > 890 \mbox { TeV } for a mean equation of state during reheating \bar { w } _ { \mathrm { reh } } = -0.3 and \rho _ { \mathrm { reh } } ^ { 1 / 4 } > 390 \mbox { GeV } for \bar { 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 confidence 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 .