Temperature of the inflaton and duration of inflation from WMAP data
  If the initial state of the inflaton field is taken to have a thermal distribution instead of the conventional zero particle vacuum state then the curvature power spectrum gets modified by a temperature dependent factor such that the fluctuation spectrum of the microwave background radiation is enhanced at larger angles. We compare this modified cosmic microwave background spectrum with Wilkinson microwave anisotropy probe data to obtain an upper bound on the temperature of the inflaton at the time our current horizon crossed the horizon during inflation. We further conclude that there must be additional e-foldings of inflation beyond what is needed to solve the horizon problem. 
Kaushik Bhattacharya, Subhendra Mohanty and Raghavan Rangarajan