Tensor spectrum of turbulence-sourced gravitational waves as a constraint on graviton mass

TL;DR

This paper investigates how a massive gravity theory affects gravitational wave spectra from early universe turbulence, providing potential constraints on graviton mass using NANOGrav data.

Contribution

It introduces a numerical study of tensor GW spectra in a dispersive massive gravity framework sourced by early universe turbulence.

Findings

Weak dependence of spatial spectral slope modifications on eddy size at QCDPT

Pronounced temporal spectral modifications in the 1--10 nHz range

Potential to constrain graviton mass using NANOGrav observations

Abstract

We consider a generic dispersive massive gravity theory and numerically study its resulting modified energy and strain spectra of tensor gravitational waves (GWs) sourced by (i) fully developed turbulence during the electroweak phase transition (EWPT) and (ii) forced hydromagnetic turbulence during the QCD phase transition (QCDPT). The GW spectra are then computed in both spatial and temporal Fourier domains. We find, from the spatial spectra, that the slope modifications are weakly dependent on the eddy size at QCDPT, and, from the temporal spectra, that the modifications are pronounced in the $1$--$10{\rm nHz}$ range -- the sensitivity range of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) -- for a graviton mass $m_{\rm g}$ in the range $2\times10^{-23}{\rm eV}\lesssim m_{\rm g}c^2\lesssim7\times10^{-22}{\rm eV}$.