Mass density perturbations from inflation with thermal dissipation

We study the power spectrum of the mass density perturbations in an inflation scenario that includes thermal dissipation. We show that the condition on which the thermal fluctuations dominate the primordial density perturbations can easily be realized even for weak dissipation, i.e., the rate of dissipation is less than the Hubble expansion. We find that our spectrum of primordial density perturbations follows a power law behavior, and exhibits a “thermodynamical” feature—the amplitude and power index of the spectrum depend mainly on the thermodynamical variable M, the inflation energy scale. Comparing this result with the observed temperature fluctuations of the cosmic microwave background, we find that both amplitude and index of the power spectrum can be fairly well fitted if $M\sim {10}^{15}–{10}^{16}\hspace{0.5em}\mathrm{GeV}.$