Log-dependent slope of scalar induced gravitational waves in the infrared regions

Abstract

We analytically calculate the scalar induced gravitational waves (SIGWs) and find a log-dependent slope of SIGW in the infrared regions (f<fc), namely nGW(f)=3-2/(fc/f), and nGW(f)=2-2/(fc/f) near the peak if the power spectrum of scalar curvature perturbation is quite narrow, where fc is roughly the frequency at the peak of SIGW. Such a log-dependent slope can be taken as a new template for distinguishing SIGW from other sources.

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