Revisiting a pre-inflationary radiation era and its effect on the CMB
  power spectrum
  We revisit the scenario where inflation is preceded by a radiation era by
considering that the inflaton too could have been in thermal equilibrium early
in the radiation era. Hence we take into account not only the effect of a
pre-inflationary era on the inflaton mode functions but also that of a frozen
thermal distribution of inflaton quanta. We initially discuss in detail the
issues relevant to our scenario of a pre-inflationary radiation dominated era
and then obtain the scalar power spectrum for this scenario. We find that the
power spectrum is free from infrared divergences. We then use the WMAP and
Planck data to determine the constraints on the inflaton comoving `temperature'
and on the duration of inflation. We find that the best fit value of the
duration of inflation is less than 1 e-folding more than what is required to
solve cosmological problems, while only an upper bound on the inflaton
temperature can be obtained.
