Universal infrared scaling of gravitational wave background spectra. (arXiv:1909.13728v2 [astro-ph.CO] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Cai_R/0/1/0/all/0/1">Rong-Gen Cai</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pi_S/0/1/0/all/0/1">Shi Pi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Sasaki_M/0/1/0/all/0/1">Misao Sasaki</a>

We study the general infrared behavior of the power spectrum of a stochastic

gravitational wave background produced by stress tensor in the form bilinear in

certain dynamical degrees of freedom. We find $Omega_{text{GW}}propto k^3$

for a very wide class of the sources which satisfy a set of reasonable

conditions. Namely, the $k^3$ scaling is universally valid when the source term

is bounded in both frequency and time, is effective in a radiation-dominated

stage, and for $k$ smaller than all the physical scales associated with the

source, like the peak frequency, peak width, and time duration, etc. We also

discuss possible violations of these conditions and their physical

implications.

We study the general infrared behavior of the power spectrum of a stochastic

gravitational wave background produced by stress tensor in the form bilinear in

certain dynamical degrees of freedom. We find $Omega_{text{GW}}propto k^3$

for a very wide class of the sources which satisfy a set of reasonable

conditions. Namely, the $k^3$ scaling is universally valid when the source term

is bounded in both frequency and time, is effective in a radiation-dominated

stage, and for $k$ smaller than all the physical scales associated with the

source, like the peak frequency, peak width, and time duration, etc. We also

discuss possible violations of these conditions and their physical

implications.

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