[Paper Review] Gravitational waves from resonant amplification of curvature perturbations during inflation

Zhi-Zhang Peng, Chengjie Fu+3 more|arXiv (Cornell University)|Jun 22, 2021

Cosmology and Gravitation Theories63 references42 citations

TL;DR

This paper investigates gravitational waves (GWs) induced by resonantly amplified curvature perturbations during inflation in a single-field inflationary model with a periodic potential structure. Using numerical simulations, it shows that GWs produced during inflation have a significantly higher peak amplitude and lower peak frequency than those generated in the radiation-dominated era, with a distinctive oscillatory feature in the ultraviolet regime when the curvature power spectrum is narrow—offering a unique signature for future space-based GW detectors like LISA and Taiji.

ABSTRACT

Parametric resonance in a single-field inflationary model with a periodic structure on the potential gives rise to curvature perturbations with large amplitudes on small scales, which could result in observable primordial black holes (PBHs) and concomitant gravitational waves (GWs) induced by curvature perturbations in the radiation-dominated era. In such a model, GWs associated with the PBH formation were investigated in Ref. [1]. In this paper, we consider a stochastic GW background sourced by inflaton perturbations resonantly amplified during inflation. We compute the energy spectra of induced GWs produced both during inflation and in the radiation-dominated era, and find that the peak of the energy spectrum of the former is much higher than that of the latter, but is located at a lower frequency. Moreover, the energy spectrum of induced GWs produced during inflation exhibits a unique oscillating character in the ultraviolet region. Both the stochastic GW backgrounds are expected to be detected by future space-based laser interferometers.

Motivation & Objective

• To investigate the production of gravitational waves (GWs) sourced by parametric resonance of inflaton perturbations during inflation in a single-field model with a periodic potential structure.
• To compute and compare the energy spectra of induced GWs produced both during inflation and in the radiation-dominated era.
• To identify unique spectral features—particularly oscillatory behavior in the ultraviolet band—that distinguish inflationary GWs from those generated post-inflation.
• To assess the detectability of these GW backgrounds with future space-based laser interferometers such as LISA and Taiji.
• To provide a complete energy spectrum profile of induced GWs for testing inflationary models with resonant amplification mechanisms.

Proposed method

• Formulates a single-field inflationary model with a periodic potential structure V(φ) = V̄(φ) + ξ cos(φ/φ*)Θ(φ−φe)Θ(φs−φ), where the periodic term triggers parametric resonance.
• Solves the inflaton background evolution under slow-roll conditions with a large field excursion, leading to oscillatory effective mass terms in the perturbation equation.
• Transforms the inflaton perturbation equation into a Mathieu-type differential equation, enabling the study of parametric resonance and exponential growth of scalar modes.
• Computes the energy spectrum of induced GWs using second-order perturbation theory, accounting for nonlinear coupling between curvature and tensor perturbations.
• Numerically evolves the system to compute the power spectrum of GWs during inflation and in the radiation-dominated era, using rescaled time and wavenumber variables.
• Analyzes the resulting GW energy spectra, focusing on peak amplitudes, peak frequencies, and spectral oscillations in the ultraviolet region for different parameter choices (ξ, φ*).

Experimental results

Research questions

• RQ1 What is the amplitude and frequency distribution of gravitational waves induced by resonantly amplified curvature perturbations during inflation in a periodic potential model?
• RQ2 How does the energy spectrum of GWs produced during inflation compare quantitatively with that produced in the radiation-dominated era?
• RQ3 Does the energy spectrum of inflationary GWs exhibit unique features—such as oscillatory behavior in the ultraviolet band—and under what conditions do they emerge?
• RQ4 Can the combined GW background from both inflation and the radiation-dominated era be detected by future space-based interferometers like LISA and Taiji?
• RQ5 What is the physical origin of the oscillatory structure in the energy spectrum of inflationary GWs, and how does it depend on the width of the curvature power spectrum?

Key findings

• The energy spectrum of gravitational waves produced during inflation exhibits a significantly higher peak amplitude than those generated in the radiation-dominated era.
• The peak frequency of inflationary GWs is much lower than that of post-inflationary GWs, providing a key discriminant for future detection.
• When the curvature power spectrum is narrow (set 1), the energy spectrum of inflationary GWs displays a distinct oscillatory feature in the ultraviolet region, absent in the radiation-dominated era.
• This oscillatory behavior diminishes and becomes undetectable when the power spectrum broadens (set 2), indicating a strong dependence on the spectral width.
• Both the inflationary and post-inflationary GW backgrounds have peak amplitudes above the sensitivity curves of LISA and Taiji, making them potentially detectable with future space-based missions.
• The total induced GW background from both eras forms a unique, multi-featured energy spectrum that can serve as a diagnostic tool for testing inflationary models with resonant amplification.