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2020

Deformation of the gravitational wave spectrum by density perturbations

Domcke, Valerie, Jinno, Ryusuke, Rubira, Henrique

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We study the effect of primordial scalar curvature perturbations on the propagation of gravitational waves over cosmic distances.

We point out that such curvature perturbations deform the isotropic spectrum of any stochastic background of gravitational waves of primordial origin through the (integrated) Sachs-Wolfe effect.
Computing the changes in the amplitude and frequency of the propagating gravitational wave induced at linear order by scalar curvature perturbations, we show that the resulting deformation of each frequency bin of the gravitational wave spectrum is described by a linearly biased Gaussian with the variance $\sigma^2 \simeq \int d\ln k \Delta_{\mathcal R}^2$, where $\Delta_{\mathcal R}^2(k)$ denotes the amplitude of the primordial curvature perturbations.
The linear bias encodes the correlations between the changes induced in the frequency and amplitude of the gravitational waves.

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