Anisotropy of the astrophysical gravitational wave background: Analytic expression of the angular power spectrum and correlation with cosmological observations

Abstract

Unresolved sources of gravitational waves are at the origin of a stochastic gravitational wave background. While the computation of its mean density as a function of frequency in a homogeneous and isotropic universe is standard lore, the computation of its anisotropies requires to understand the coarse graining from local systems, to galactic scales and then to cosmology. An expression of the gravitational wave energy density valid in any general spacetime is derived. It is then specialized to a perturbed Friedmann-Lemaître spacetime in order to determine the angular power spectrum of this stochastic background as well as its correlation with other cosmological probes, such as the galaxy number counts and weak lensing. Our result for the angular power spectrum also provides an expression for the variance of the gravitational wave background.

Polarization of a stochastic gravitational wave background through diffusion by massive structures

“…(3.10), (3.11) and (3.12) in terms of matter and metric perturbations. Polarization is therefore a stochastic quantity which can be characterized statistically in terms of its two-point function, like the energy density of the GW background in [59]. Moreover, it will cross-correlate with GW energy density and with other cosmological probes such as the galaxy distribution and weak lensing.…”

“…In [59] an analytic framework is presented to describe and compute the anisotropies in the observed energy density of the AGWB, taking into account the presence of inhomogeneities in the matter distribution and in the geometry of the observed universe. In [60] an alternative (more geometrical) derivation of the result of [59] is presented, and first numerical predictions for the amplitude of anisotropies for the contribution of the background coming from black hole mergers can be found in [61]. For an astrophysical background, the origin of anisotropies is two fold: first, sources are not isotropically distributed and second, a GW signal, once emitted, is deflected by structures.…”

Estimating the angular power spectrum of the gravitational-wave background in the presence of shot noise

“…Since the components of CBCs are the results of stellar evolution, they should reside in galaxies, 1 and the AGWB should trace the distribution of galaxies throughout the local Universe. There has therefore been significant recent interest in AGWB anisotropies [15][16][17][18][19][20][21] and associated observational searches [22][23][24] and data-analysis methods [25][26][27][28][29][30][31], as these might provide an entirely new probe of galaxy clustering and large-scale structure (LSS).…”

Gravitational wave anisotropies from primordial black holes

“…Even assuming a completely homogeneous and isotropic SGWB at its production, these GWs propagate in a perturbed universe. As a consequence, the GW signal arriving to Earth has angular anisotropies [37][38][39][40][41][42][43] which are non-Gaussian [44]. In addition, as we show and quantify in this work, the GW production itself has some degree of anisotropy and non-Gaussianity.…”