Analytic integral solutions for induced gravitational waves

Abstract

We present analytic integral solutions for the second-order induced gravitational waves (GWs). After presenting all the possible second-order source terms, we calculate explicitly the solutions for the GWs induced by the linear scalar and tensor perturbations during matter- and radiation-dominated epochs.

(v1) 29 pages, 6 figures; (v2) AASTeX, discussions expanded including the RD solutions, references added, to appear in Astrophysical Journal

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