Cosmic inflation and model comparison

We analyze the implications for inflation of the recently released Planck Cosmic Microwave Background data and explain why the single-field slow-roll scenarios with minimal kinetic terms are favored. Within this class of models, we show how Bayesian model comparison can be used to further exclude about one third of the inflationary scenarios. We also study the end of inflation and show that Planck can already constrain the reheating phase. Finally, we conclude by discussing how future missions will be able to improve our knowledge of the inflationary mechanism