Thermalized axion inflation: Natural and monomial inflation with small r

A safe way to reheat the Universe, in models of natural and quadratic inflation, is through shift symmetric couplings between the inflaton phi and the Standard Model (SM), since they do not generate loop corrections to the potential V(phi). We consider such a coupling to SM gauge fields, of the form phi F (F) over tilde /f, with sub-Planckian f. In this case, gauge fields can be exponentially produced already during inflation and thermalize via interactions with charged particles, as pointed out in previous work. This can lead to a plasma of temperature T during inflation, and the thermal masses gT of the gauge bosons can equilibrate the system. In addition, inflaton perturbations delta phi. can also have a thermal spectrum if they have sufficiently large cross sections with the plasma. In this case, inflationary predictions are strongly modified: (1) scalar perturbations are thermal, and so enhanced over the vacuum, leading to a generic way to suppress the tensor-to-scalar ratio r; (2) the spectral index is n(s) - 1 = eta - 4 epsilon. After presenting the relevant conditions for thermalization, we show that thermalized natural and monomial models of inflation agree with present observations and have r approximate to 10(-3) - 10(-2), which is within reach of next generation CMB experiments.