Thermalized axion inflation: Natural and monomial inflation with small r

Abstract

A safe way to reheat the Universe, in models of natural and quadratic inflation, is through shift symmetric couplings between the inflaton $\ensuremath{\phi}$ and the Standard Model (SM), since they do not generate loop corrections to the potential $V(\ensuremath{\phi})$. We consider such a coupling to SM gauge fields, of the form $\ensuremath{\phi}F\stackrel{\texttildelow{}}{F}/f$, 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 $\ensuremath{\delta}\ensuremath{\phi}$ 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 ${n}_{s}\ensuremath{-}1=\ensuremath{\eta}\ensuremath{-}4\ensuremath{\epsilon}$. After presenting the relevant conditions for thermalization, we show that thermalized natural and monomial models of inflation agree with present observations and have $r\ensuremath{\approx}{10}^{\ensuremath{-}3}\ensuremath{-}{10}^{\ensuremath{-}2}$, which is within reach of next generation CMB experiments.