Parametric Resonance and Cosmological Gravitational Waves

TL;DR

This paper studies how quantum fluctuations during a parametric resonance-driven transition from inflation to radiation domination produce gravitational waves, revealing that the resonance itself leaves no distinctive spectral imprint.

Contribution

It introduces a method using continuous Bogoliubov coefficients to calculate the gravitational wave spectrum, showing the resonance's minimal direct impact on the spectrum's features.

Findings

Resonance causes no distinctive spectral imprint beyond a frequency shift.

Main spectral features originate from the inflaton field.

Spectrum features appear at MHz/GHz frequencies.

Abstract

We investigate the production of gravitational waves due to quantum fluctuations of the vacuum during the transition from the inflationary to the radiation-dominated eras of the universe, assuming this transition to be dominated by the phenomenon of parametric resonance. The energy spectrum of the gravitational waves is calculated using the method of continuous Bogoliubov coefficients, which avoids the problem of overproduction of gravitons at large frequencies. We found, on the sole basis of the mechanism of quantum fluctuations, that the resonance field leaves no explicit and distinctive imprint on the gravitational-wave energy spectrum, apart an overall upward or downward translation. Therefore, the main features in the spectrum are due to the inflaton field, which leaves a characteristic imprint at frequencies of the order of MHz/GHz.