Particle decay during inflation: Self-decay of inflaton quantum fluctuations during slow roll

Abstract

Particle decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small $\ensuremath{\Delta}$ expansion. $\ensuremath{\Delta}$ measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow-roll inflation, $\ensuremath{\Delta}$ is a simple function of the slow-roll parameters ${ϵ}_{V},{\ensuremath{\eta}}_{V}$. We find that quantum fluctuations can self-decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-decay of the inflaton quantum fluctuations during slow-roll inflation. For wavelengths deep inside the Hubble radius the decay is enhanced by the emission of ultrasoft collinear quanta, i.e., bremsstrahlung radiation of superhorizon quanta which becomes the leading decay channel for physical wavelengths $H\ensuremath{\ll}{k}_{\mathrm{p}\mathrm{h}}(\ensuremath{\eta})\ensuremath{\ll}H/({\ensuremath{\eta}}_{V}\ensuremath{-}{ϵ}_{V})$. The decay of short wavelength fluctuations hastens as the physical wave vector approaches the horizon. Superhorizon fluctuations decay with a power law ${\ensuremath{\eta}}^{\ensuremath{\Gamma}}$ in conformal time where in terms of the amplitude of curvature perturbations ${△}_{\mathcal{R}}^{2}$, the scalar spectral index ${n}_{s}$, the tensor to scalar ratio $r$ and slow-roll parameters: $\ensuremath{\Gamma}\ensuremath{\simeq}[32{\ensuremath{\xi}}_{V}^{2}{△}_{\mathcal{R}}^{2}/({n}_{s}\ensuremath{-}1+\frac{r}{4}{)}^{2}][1+\mathcal{O}({ϵ}_{V},{\ensuremath{\eta}}_{V})]$. The behavior of the growing mode ${\ensuremath{\eta}}^{{\ensuremath{\eta}}_{V}\ensuremath{-}{ϵ}_{V}+\ensuremath{\Gamma}}/\ensuremath{\eta}$ features an anomalous scaling dimension $\ensuremath{\Gamma}$. We discuss the implications of these results for scalar and tensor perturbations as well as for non-Gaussianities in the power spectrum. The recent Wilkinson Map Anisotropy Probe data suggests $\ensuremath{\Gamma}\ensuremath{\gtrsim}3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$.