Warm inflation dissipative effects: predictions and constraints from the Planck data

Abstract: We explore the warm inflation scenario theoretical predictions looking at two different dissipative regimes for several representative primordial potentials. As it is well known, the warm inflation is able to decrease the tensor-to-scalar ratio value, rehabilitating several primordial potential ruled out in the cold inflation context by the recent cosmic microwave background data. Here we show that it is also able to produce a running of the running $n_s"$ positive and within the Planck data limits. This is very remarkable since the standard cold inflation model is unable to justify the current indication of a positive constraint on $n_s"$. We achieve a parameterization for the primordial power spectrum able to take into account higher order effects as the running of the spectral index and the running of the running, and we perform statistical analysis using the most up-to-date Planck data to constrain the dissipative effects. We find that the warm inflation can explain the current observables with a good statistical significance, even for those potentials ruled out in the simplest cold inflation scenario.