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

TL;DR

This work tackles particle decay during inflation by combining a dynamical renormalization group (DRG) approach with a small infrared regulator Δ to study self-decay of inflaton fluctuations in quasi-de Sitter slow-roll. It shows that minimally coupled, light fields exhibit enhanced infrared effects, including bremsstrahlung of ultrasoft quanta, leading to decay laws for both superhorizon and subhorizon modes; the decay rate Γ is explicitly tied to slow-roll parameters and the curvature perturbation amplitude Δ^2_R. The inflaton’s self-decay yields an anomalous dimension for the growing mode of superhorizon fluctuations, with Γ expressible as Γ = (8 ξ_V^2 Δ^2_R)/(ε_V−η_V)^2 (to leading order), connecting quantum decay to observable inflationary parameters. The results illuminate potential corrections to scalar and tensor power spectra and offer a pathway to non-Gaussianity through the same cubic interactions, while highlighting the need for gauge-invariant treatments and full graviton self-energy calculations to solidify observational implications.

Abstract

Particle decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small Delta expansion. Delta measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow roll inflation, Delta is a simple function of the slow roll parameters epsilon_V, 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<<k_{ph}(eta)<<H/(eta_V-eps_V). The decay of short wavelength fluctuations hastens as the physical wave vector approaches the horizon. Superhorizon fluctuations decay with a power law eta^Gamma in conformal time where in terms of the amplitude of curvature perturbations Delta^2_R, the scalar spectral index n_s, the tensor to scalar ratio r and slow roll parameters: Gamma \simeq [32 xi^2_V Delta^2_R]/ /(n_s-1+r/4)^2.The behavior of the growing mode eta^{eta_V-epsilon_V+Gamma}/eta features an anomalous scaling dimension Gamma. We discuss the implications of these results for scalar and tensor perturbations and for non-gaussianities in the power spectrum. The recent WMAP data suggests Gamma >3.6 10^{-9}.

Figures (5)

• Figure 1: Self energies: Fig.(a) depicts the self energy contribution from a loop of $\varphi$ particles, Fig. (b) depicts the self-energy from the self-interaction of the inflaton.
• Figure 2: Decay of the field $\phi$ (solid line) for $k=0$ into superhorizon modes of the field $\varphi$
• Figure 3: Infrared contributions to $\phi \rightarrow \varphi \varphi$. The external particle has a wavelength deep inside the horizon but one of the intermediate lines has superhorizon wavelengths. This process is identified as bremsstrahlung radiation of superhorizon quanta.
• Figure 4: Self-decay of quantum fluctuations of the inflaton. All lines correspond to the field $\phi$, i.e, the quantum fluctuations of the inflaton.
• Figure 5: Equal time three point function $\langle \chi(\vec{k},\eta) \; \chi(\vec{q},\eta) \; \chi(-\vec{k}-\vec{q},\eta)\rangle$ in the Born approximation. The time coordinate $\eta_1$ of the vertex is integrated.