Effects of particle production during inflation

TL;DR

This paper analyzes how particle production during inflation, driven by coupling the inflaton to a massive scalar field, alters the primordial curvature perturbation spectrum. Using analytic techniques and numerical integration of the perturbation equations, it shows that a temporary slow-roll violation at t0 induces oscillations in the small-scale portion of the spectrum P_R(k), with no accompanying large-scale step. The oscillation amplitude scales with the number of coupled fields N, the mediator mass m_varphi, and the coupling g^2, and the period is set by the horizon-crossing wavenumber at the transition. The results provide a general framework for features arising from sudden changes in the inflaton potential and suggest potential observational signatures in the CMB and large-scale structure.

Abstract

The impact of particle production during inflation on the primordial curvature perturbation spectrum is investigated both analytically and numerically. We obtain an oscillatory behavior on small scales, while on large scales the spectrum is unaffected. The amplitude of the oscillations is proportional to the number of coupled fields, their mass, and the square of the coupling constant. The oscillations are due a discontinuity in the second time derivative of the inflaton, arising from a temporary violation of the slow-roll conditions. A similar effect on the power spectrum should be produced also in other inflationary models where the slow-roll conditions are temporarily violated.

Figures (5)

• Figure 1: $\dot\phi(t)/(m_p m_{\phi})$ is plotted for $-0.1<m_{\phi}(t-t_0)<0.5$. The solid line corresponds to $N=1$, the small dashed line to $N=8$, and the long dashed line to $N=16$.
• Figure 2: $\ddot\phi(t)/(m_p m^2_{\phi})$ is plotted for $-0.1<m_{\phi}(t-t_0)<0.5$. The parameters are the same as Fig. 1.
• Figure 3: $P_{{\mathcal{R}}}^{1/2}(k)$ is plotted for $3\times10^{-2}<k/(a_0 H_0)<50$ in the case of $N=8$. The solid line is the numerical result, the dashed line is the analytical approximation, and the long dashed line is the spectrum in the absence of particle production.
• Figure 4: The same as Fig. 3, but in the case of $N=16$.
• Figure 5: $P^{1/2}_{\mathcal{R}}(k)$ in the cases of both $N=8$ and $N=16$ are plotted for $3\times 10^{-2}<k/(a_0 H_0)<50$. Clearly the amplitude of oscillations is larger for larger $N$, approximately in proportion to $N$. The long dashed line is the spectrum in the absence of coupling.