Warm Inflation

I show here that there are some interesting differences between the predictions of warm and cold inflation models focusing in particular upon the scalar spectral index n s and the tensor-to-scalar ratio r. The first thing to be noted is that the warm inflation models in general predict a vanishingly small value of r. Cold inflationary models with the potential V = M 4 ( ϕ / M P ) p and a number of e-folds N = 60 predict δ n s C ≡ 1 − n s ≈ ( p + 2 ) / 120 , where n s is the scalar spectral index, while the corresponding warm inflation models with constant value of the dissipation parameter Γ predict δ n s W = [ ( 20 + p ) / ( 4 + p ) ] / 120 . For example, for p = 2 this gives δ n s W = 1.1 δ n s C . The warm polynomial model with Γ = V seems to be in conflict with the Planck data. However, the warm natural inflation model can be adjusted to be in agreement with the Planck data. It has, however, more adjustable parameters in the expressions for the spectral parameters than the corresponding cold inflation model, and is hence a weaker model with less predictive force. However, it should be noted that the warm inflation models take into account physical processes such as dissipation of inflaton energy to radiation energy, which is neglected in the cold inflationary models