Abstract
A future detection of the Stochastic Gravitational Wave Background (SGWB) with GW experiments is expected to open a new window on early universe cosmology and on the astrophysics of compact objects. In this paper we study SGWB anisotropies, that can offer new tools to discriminate between different sources of GWs. In particular, the cosmological SGWB inherits its anisotropies both (i) at its production and (ii) during its propagation through our perturbed universe. Concerning (i), we show that it typically leads to anisotropies with order one dependence on frequency. We then compute the effect of (ii) through a Boltzmann approach, including contributions of both large-scale scalar and tensor linearized perturbations. We also compute for the first time the three-point function of the SGWB energy density, which can allow one to extract information on GW non-Gaussianity with interferometers. Finally, we include non-linear effects associated with long wavelength scalar fluctuations, and compute the squeezed limit of the 3-point function for the SGWB density contrast. Such limit satisfies a consistency relation, conceptually similar to what found in the literature for the case of CMB perturbations.
Highlights
The current ground-based interferometers are close to reaching the expected sensitivity to detect the stochastic gravitational wave background (SGWB) from unresolved astrophysical sources [1]
Since the phase does not affect the GW energy density, we argue that the energy density is a much better variable to study the statistics of the SGWB
V we review one physical mechanism that can result in a sizeable cosmological SGWB with some degree of anisotropy
Summary
The current ground-based interferometers are close to reaching the expected sensitivity to detect the stochastic gravitational wave background (SGWB) from unresolved astrophysical sources [1]. An analysis of detection methods of non-Gaussianity in a GWB induced by short-duration signals has been done in [26], while in [27,28] it has been studied how to use higher-order cumulants to characterize properties of nonGaussianity in the AGWB (see [29] for a recent analysis) In light of this fact, a measurement of nonGaussianity would be a signal of large scale coherency, that would likely point to a cosmological origin of the signal. We make use of a powerful method first introduced by Weinberg in [31], which focuses on adiabatic systems, and identifies the effects of long modes with an appropriate coordinate transformation Applying this method to our setup, we compute how nonlinearities induce a nonvanishing squeezed limit of the 3-point function for the SGWB density contrast. Part of the results contained in the present work were summarized in [32]
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