Fluctuations in Hill's equation parameters and application to cosmic reheating

TL;DR

This paper explores how stochastic fluctuations in Hill's equation parameters, which describe parametric resonance during cosmic reheating, can significantly enhance particle production, impacting early Universe cosmology models.

Contribution

It introduces a novel analysis of stochastic effects on Hill's equation parameters, revealing their role in broadening resonance stability bands and boosting reheating efficiency.

Findings

Stochastic fluctuations can significantly increase particle production.

Noise broadens the resonance stability bands.

Analytical and numerical methods confirm the impact of noise.

Abstract

Cosmic inflation provides a compelling framework for explaining several observed features of our Universe, but its viability depends on an efficient reheating phase that converts the inflaton's energy into Standard Model particles. This conversion often proceeds through non-perturbative mechanisms such as parametric resonance, which is described by Hill's equation. In this work, we investigate how stochastic fluctuations in the parameters of Hill's equation can influence particle production during reheating. We show that such fluctuations can arise from couplings to light scalar fields, and can significantly alter the stability bands in the resonance structure, thereby enhancing the growth of fluctuations and broadening the region of efficient energy transfer. Using random matrix theory and stochastic differential equations, we decompose the particle growth rate into deterministic and noise-induced components and demonstrate analytically and numerically that even modest noise leads to substantial particle production in otherwise stable regimes. These results suggest that stochastic effects can robustly enhance the efficacy of reheating across a wide swath of parameter space, with implications for early Universe cosmology, UV completions involving multiple scalar fields, and the resolution of the cosmological moduli problem.