Probing Planckian physics: resonant production of particles during inflation and features in the primordial power spectrum

TL;DR

This paper investigates resonant production of a Planck-scale fermion during inflation by coupling the inflaton to a massive state, showing that a transient extraction of inflaton energy can produce a sharp spike in the primordial power spectrum $\delta_H(k)$ with width smaller than one e-fold. The analysis combines analytic approximations for the production efficiency and inflaton dynamics with full numerical results that include backreaction, revealing that the spike amplitude scales roughly as $N\lambda^{5/2}$ until backreaction constrains production. The authors provide practical expressions for the spike, discuss how to map it to present-day observables in $P(k)$ and $C_\ell$, and evaluate the prospects for detecting such features with CMB and LSS surveys, concluding that observations could probe Planck-scale physics through resonant couplings to heavy states. If observed, these spikes would have important implications for reconstructing the inflaton sector and could bias standard cosmological parameter estimation if not accounted for. The work thus offers a concrete, testable link between high-scale particle physics and observable cosmological perturbations.

Abstract

The phenomenon of resonant production of particles {\it after} inflation has received much attention in the past few years. In a new application of resonant production of particles, we consider the effect of a resonance {\em during} inflation. We show that if the inflaton is coupled to a massive particle, resonant production of the particle during inflation modifies the evolution of the inflaton, and may leave an imprint in the form of sharp features in the primordial power spectrum. Precision measurements of microwave background anisotropies and large-scale structure surveys could be sensitive to the features, and probe the spectrum of particles as massive as the Planck scale.

Figures (11)

• Figure 1: The spectrum of produced fermions around $\eta=\eta_*$ as a function of physical momentum $k_p$. Also shown is the analytic approximation.
• Figure 2: The numerical result for the evolution of $\dot{\phi}$, including the effect of resonant particle production, is shown by the solid curve. Also shown by the dashed curve (nearly indistinguishable from the numerical result) is the analytic expression of Eq. (\ref{['eq:deltaphidot']}).
• Figure 3: Analytic solutions for $\dot{\phi}$ assuming no decay of the fermion (the solid curve) and with decay parameters $\sqrt{\alpha\lambda\dot{\phi}_*}/m_\phi = 10^3$, $10^2$, and $10^1$. The feature disappears as $\sqrt{\alpha\lambda\dot{\phi}_*}/m_\phi \rightarrow \infty$, and as the quantity approaches zero, we recover the result of no decay.
• Figure 4: Resonant particle production produces a peak in the perturbation spectrum as shown in the figure. The solid curve is the numerical result. the dashed curve is the analytic form of Eq. (\ref{['eq:deltaanalytic']}). Finally, the dotted curve indicates the power spectrum in the absence of resonant particle creation.
• Figure 5: The evolution of $H$ and $\phi$ in this model is not noticeably altered by resonant fermion production. Only small inflections in $\phi(t)$ and $H(t)$ are noticeable around the time of resonance, $t\simeq t_*$ where $t_*$ is the time when $\phi=\phi_*$.