Gravitational waves induced by scalar perturbations with a lognormal peak
By Shi Pi, Misao Sasaki. Journal of Cosmology and Astroparticle Physics, 2020
186 citations recorded by the source corpus.
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 ΩGW 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= 2k*/√3. On the infrared (IR) side of the spectrum, we find power-law behavior with a break at k=kb in the power-law index where it chages from k3 on the far IR side to k2 on the near IR side. We find the ratio of the break frequency to the peak frequency is determined by Δ as fb/fp≈√3Δ, where fb and fp 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 ΩGW for both narrow and broad cases. Our results will provide a useful tool in searching for the induced GW signals in the coming decades.
Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2e09359f41d1941d0a9ab8fe2d5537c62c8a2294
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Citations in the corpus
- Solar-mass primordial black holes explain NANOGrav hint of gravitational waves (2020, methodology): “In the case of the log-normal power spectrum, the full (approximate) analytic formula of ΩGW,c(f) is available [49] although we compute it numerically with the aid of an extrapolation into the IR tail using the formula of Ref.”
- Oscillations in the stochastic gravitational wave background from sharp features and particle production during inflation (2020, methodology): “Following [55], for a narrow-peaked scalar power spectrum the amplitude of ΩGW at the principal peak can be estimated by taking the result for a δ-peak and smoothing Ω GW over an appropriate scale.”