Non-Gaussianity as a signature of thermal initial condition of inflation
  We study non-Gaussianities in the primordial perturbations in single field
inflation where there is radiation era prior to inflation. Inflation takes
place when the energy density of radiation drops below the value of the
potential of a coherent scalar field. We compute the thermal average of the
two, three and four point correlation functions of inflaton fluctuations. The
three point function is proportional to the slow roll parameters and there is
an amplification in $f_{NL}$ by a factor of 65 to 90 due to the contribution of
the thermal bath, and we conclude that the bispectrum is in the range of
detectability with the 21-cm anisotropy measurements. The four point function
on the other hand appears in this case due to the thermal averaging and the
fact that thermal averaging of four-point correlation is not the same as the
square of the thermal averaging of the two-point function. Due to this fact
$\tau_{NL}$ is not proportional to the slow-roll parameters and can be as large
as -42. The non-Gaussianities in the four point correlation of the order 10 can
also be detected by 21-cm background observations. We conclude that a signature
of thermal inflatons is a large trispectrum non-Gaussianity compared to the
bispectrum non-Gaussianity.
