Scalar perturbation spectra from warm inflation

We present a numerical integration of the cosmological scalar perturbation equations in warm inflation. The initial conditions are provided by a discussion of the thermal fluctuations of an inflaton field and thermal radiation using a combination of thermal field theory and thermodynamics. The perturbation equations include the effects of a damping coefficient Gamma and a thermodynamic potential V. We give an analytic expression for the spectral index of scalar fluctuations in terms of a new slow-roll parameter constructed from Gamma. A series of toy models, inspired by spontaneous symmetry breaking and a known form of the damping coefficient, lead to a spectrum with n(s)>1 on large scales and n(s)<1 on small scales.