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

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 range — the sensitivity range of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) — for a graviton mass in the range 2×10-23 c27×10-22.

Modified propagation of gravitational waves from the early radiation era

“…The effect of massive gravitons could be included by adding a m g = 0 term multiplying to h ij in equation (2.3), as done in ref. [70], but we omit it in the present work. Equation (2.3) can be recast in a simplified equation by introducing the new variable [51,56,60], with…”

“…Therefore, we have adapted the Pencil Code to evolve an initial GW spectrum in the absence of sources with a spectral shape and amplitude based on those obtained in previous studies (see, e.g., refs. [70,84]). Hence, equation (2.3) is solved in one dimension (i.e., in k > 0) in order to improve the efficiency of the code when studying the propagation of a GW background along the history of the universe.…”

“…For a similar study concerning the effects of m g , see ref. [70]. Our focus on the cosmological effects of α M is motivated by its less stringent constraints compared to α T , and its accumulated effects over cosmic history.…”