Observational constraints on particle production during inflation

TL;DR

This paper analyzes how resonant particle production during inflation can imprint a localized, step-like feature in the primordial curvature power spectrum $P_{ mathcal{R}}(k)$ by coupling the inflaton to a massive field. Using a Hartree-approximation framework, it derives the backreaction that transfers energy from the inflaton to produced particles, alters the evolution of curvature perturbations, and generates a characteristic step with high-frequency oscillations in $P_{ mathcal{R}}(k)$, quantified by the effective height $N_{ m eff}$ and location $k_{ m break}$. A detailed numerical treatment of the coupled system, including Bogoliubov coefficients and two-point correlators, shows that the step is most pronounced for certain $k$-ranges and that the large-scale curvature perturbation is suppressed on superhorizon scales due to entropy production. When contrasted with CMB and 2dFGRS data, the study finds robust upper limits on $N_{ m eff}$ (e.g., $\sim0.3$ at 2$\sigma$ for $k_{ m break}\sim10^{-3}-10^{-2}\,h\mathrm{Mpc}^{-1}$), with window-function smoothing of sharp features reducing direct detectability in the CMB but enabling stronger joint constraints. The results underscore a general link between rapid EOS changes during inflation and observable features in the primordial spectrum, while highlighting methodological limitations and the potential for future data (e.g., Planck) to tighten constraints on such scenarios.

Abstract

Resonant particle production, along with many other physical processes which change the effective equation of state (EOS) during inflation, introduces a step-like feature in the primordial power spectrum. We calculate observational constraints on resonant particle production, parameterised in form of an effective step height, N_eff and location in k-space, k_break. Combining data from the cosmic microwave background and the 2dF Galaxy Redshift Survey yields strong constraints in some regions of parameter space, although the range in k-space which can be probed is restricted to k ~ 0.001 - 0.1 h Mpc^-1. We also discuss the implications of our findings for general models which change the effective EOS during inflation.

Figures (5)

• Figure 1: The number density and the time development of the correlation function, which roughly speaking is the same as the backreaction term. Both are compared to the analytic approximations, and in general there are very good agreement. The boxcar smoothing, was done to emphasise the secular evolution by canceling out the oscillations.
• Figure 2: The power spectra from different models. In the right plot the effective number of degrees of freedom is so high that a perturbative calculation of the step height cannot be trusted, while the left plot shows the monotonic evolution of step height for weaker couplings.
• Figure 3: The effect of convolving matter power spectra with the 2dFGRS window function. The black lines are the matter power spectra computed with CMBFAST for four different values of $k_{\rm break}$, the red lines are the corresponding spectra after convolution with the window function. The vertical bars are the 2dFGRS power spectrum data points.
• Figure 4: 68% and 95% confidence exclusion plot of the parameters $N_{\rm eff}$ and $k_{\rm break}$ for the four different cases described in the text. The horizontal lines show the range in $k$-space covered by various data sets. CMB data have been converted from $k$ to $l$ using the approximate prescription $l \simeq 2 k/H_0$.
• Figure 5: Ratio of $C_l$ for model with step to model without step. The full line is the precise numerical calculation and the dashed is the approximation in Eq. (\ref{['eq:ratio']}).