Gravitational Waves as a Source of Large-Scale White Noise: New Constraints

Abstract

A stochastic gravitational wave (GW) background sources a shear in the flow of cosmic fluid which, through non-linear mode coupling, generates large-scale white noise (LSWN) in the kurvature density field. Building on the LSWN framework of our previous work, we derive the amplitude of this GW-induced LSWN and translate the observational non-detection of LSWN into bounds on the production redshift and density of gravity waves. In particular, a minimal constraint on gravity waves with $z=0$ density parameter $\hat{I}{\text{c◯}}_{GW0}^{\ast }$ in frequency band $f_{\ast }$ generated at redshift $z_{\ast }$ must satisfy ${z_{\ast }}^2\hat{I}{\text{c◯}}_{GW0}^{\ast }<5\times 10^7(f_{\ast }/\mathrm{nHz}{)}^{3/2}$. This, for example, precludes the gravity waves recently detected by pulsar timing arrays \cite{NANOGrav:2023hvm} from being present before $z_{\ast }\sim 10^8$, long after the quark hadron phase transition. While orders of magnitude stronger than other constraints on gravity waves, this is a minimal LSWN constraint as realistic modeling of early universe gravity wave production, including the granularity of the gravity-wave sources and the LSWN produced by the associated acoustic waves would probably tighten this constraint by orders of magnitude.

16 pages 2 figures

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