Causal Gravitational-Wave Production Does Not Generate Infrared Adiabatic Curvature

Abstract

Short tensor modes can generate a white noise contribution to the local scalar $K=8\pi G\rho /3-{\theta }^2/9$, but this does not induce an infrared-enhanced adiabatic curvature spectrum. For a conserved causal source, analyticity of the longitudinal velocity correlator requires $P_V=\mathcal{O}(k^2)$, hence $P_{\mathcal{R}}=\mathcal{O}(k^0)$ and ${\Delta }_{\mathcal{R}}^2=\mathcal{O}(k^3)$, excluding the ${\Delta }_{\mathcal{R}}^2\propto k^{-1}$ relic. We also construct a conserved conversion of radiation into gravitational waves: the white field resides in a compensated entropy mode, and the fluid response cancels the slowly decaying $a^{-2}$ relic. Adiabatic bounds on such sources are therefore source- and matching-dependent.

4 pages