Leading-order nonlinear gravitational waves from reheating magnetogeneses

TL;DR

This paper investigates the impact of nonlinear effects on gravitational waves generated during reheating magnetogenesis, revealing that nonlinear contributions can significantly alter the GW spectrum and polarization, with implications for future detection.

Contribution

It provides the first detailed numerical analysis of leading-order nonlinear gravitational waves from electromagnetic stress during reheating magnetogenesis, including polarization effects and parameterizations.

Findings

Nonlinear GW energy exceeds linear predictions.

Nonlinear effects decrease GW polarization proportionally to EM energy density.

Parameterizations of GW energy difference and polarization suppression are provided.

Abstract

We study the leading-order nonlinear gravitational waves (GWs) produced by an electromagnetic (EM) stress in reheating magnetogenesis scenarios. Both nonhelical and helical magnetic fields are considered. By numerically solving the linear and leading-order nonlinear GW equations, we find that the GW energy from the latter is usually larger. We compare their differences in terms of the GW spectrum and parameterize the GW energy difference due to the nonlinear term, $\Delta\mathcal{E}_{\rm GW}$, in terms of EM energy $\mathcal{E}_{\rm EM}$ as $\Delta\mathcal{E}_{\rm GW}=(\tilde p\mathcal{E}_{\rm EM}/k_*)^3$, where $k_*$ is the characteristic wave number, $\tilde p=0.84$ and $0.88$ are found in the nonhelical and helical cases, respectively, with reheating around the QCD energy scale, while $\tilde p=0.45$ is found at the electroweak energy scale. We also compare the polarization spectrum of the linear and nonlinear cases and find that adding the nonlinear term usually yields a decrease in the polarization that is proportional to the EM energy density. We parameterize the fractional polarization suppression as $|\Delta \mathcal{P}_{\rm GW}/\mathcal{P}_{\rm GW}|=\tilde r \mathcal{E}_{\rm EM}/k_*$ and find $\tilde r = 1.2 \times 10^{-1}$, $7.2 \times 10^{-4}$, and $3.2 \times 10^{-2}$ for the helical cases with reheating temperatures $T_{\rm r} = 300 {\rm TeV}$, $8 {\rm GeV}$, and $120 {\rm MeV}$, respectively. Prospects of observation by pulsar timing arrays, space-based interferometers, and other novel detection proposals are also discussed.