Constraining Warm Inflation with CMB data

We confront the warm inflation observational predictions directly with the latest CMB data. We focus on a linear temperature (T) dissipative coefficient combined with the simplest model of inflation, a quartic chaotic potential. Although excluded in its standard cold inflation version, dissipation reduces the tensor-to-scalar ratio and brings the quartic chaotic model within the observable allowed range. We will use the CosmoMC package to derive constraints on the model parameters: the combination of coupling constants giving rise to dissipation, the effective number of relativistic degrees of freedom contributing to the thermal bath, and the quartic coupling in the inflaton potential. We do not assume a priori a power-law primordial spectrum, neither we fix the no. of e-folds at the horizon exit. The relation between the no. of e-folds and the comoving scale at horizon crossing is derived from the dynamics, depending on the parameters of the model, which allows us to obtain the $k$-dependent primordial power spectrum. We study the two possibilities considered in the literature for the spectrum, with the inflaton fluctuations having a thermal or a non-thermal origin, and discuss the ability of the data to constraint the model parameters.