Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak

Shi Pi; Misao Sasaki

doi:10.1088/1475-7516/2020/09/037

paper

Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak

arXiv:2005.12306 · doi:10.1088/1475-7516/2020/09/037

Abstract

We study the stochastic gravitational wave (GW) background induced by the primordial scalar perturbation with the spectrum having a lognormal peak of width $Δ$ at $k = k_{*}$ . We derive an analytical formula for the GW spectrum $Ω_{GW}$ for both narrow ( $Δ ≪ 1$ ) and broad ( $Δ ≳ 1$ ) peaks. In the narrow-peak case, the spectrum has a double peak feature with the sharper peak at $k = 2 k_{*} / 3$ . On the infrared (IR) side of the spectrum, we find power-law behavior with a break at $k = k_{b}$ in the power-law index where it chages from $k^{3}$ on the far IR side to $k^{2}$ on the near IR side. We find the ratio of the break frequency to the peak frequency is determined by $Δ$ as $f_{b} / f_{p} \approx 3 Δ$ , where $f_{b}$ and $f_{p}$ are the break and peak frequencies, respectively. In the broad-peak case, we find the GW spectrum also has a lognormal peak at $k = k_{*}$ but with a smaller width of $Δ/ 2$ . Using these derived analytic formulae, we also present expressions for the maximum values of $Ω_{GW}$ for both narrow and broad cases. Our results will provide a useful tool in searching for the induced GW signals in the coming decades.

arXiv comment15 pages, 3 figures. Some figures redrawn. References added and reorganized. Accepted for JCAP

Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak

Abstract

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