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We present the first predictions for the angular power spectrum of the astrophysical gravitational wave background constituted of the radiation emitted by all resolved and unresolved astrophysical sources. Its shape and amplitude depend on both the astrophysical properties on galactic scales and on cosmological properties. We show that the angular power spectrum behaves as $C_{ell}propto 1/{ell}$ on large scales and that relative fluctuations of the signal are of order 30% at 100 Hz. We also present the correlations of the astrophysical gravitational wave background with weak-lensing and galaxy distribution. These numerical results pave the way to the study of a new observable at the crossroad between general relativity, astrophysics and cosmology.
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There has been much recent interest in studying anisotropies in the astrophysical gravitational-wave (GW) background, as these could provide us with interesting new information about galaxy clustering and large-scale structure. However, this information is obscured by shot noise, caused by the finite number of GW sources that contribute to the background at any given time. We develop a new method for estimating the angular spectrum of anisotropies, based on the principle of combining statistically-independent data segments. We show that this gives an unbiased estimate of the true, astrophysical spectrum, removing the offset due to shot noise power, and that in the limit of many data segments, it is the most efficient (i.e. lowest-variance) estimator possible.
In the literature different approaches have been proposed to compute the anisotropies of the astrophysical gravitational wave background. The different expressions derived, although starting from our work Cusin, Pitrou, Uzan, Phys.Rev.D96, 103019 (2017) [1], seem to differ. This article compares the various theoretical expressions proposed so far and provides a separate derivation based on a Boltzmann approach. We show that all the theoretical formula in the literature are equivalent and boil down to the one of Ref. [1] when a proper matching of terms and integration by parts are performed. The difference between the various predictions presented for anisotropies in a cosmological context can only lie in the astrophysical modeling of sources, and neither in the theory nor in the cosmological description of the large scale structures. Finally we comment on the gauge invariance of expressions.
We calculate the noise induced in the anisotropies of the astrophysical gravitational-wave background by finite sampling of both the galaxy distribution and the compact binary coalescence event rate. This shot noise leads to a scale-invariant bias term in the angular power spectrum $C_ell$, for which we derive a simple analytical expression. We find that this bias dominates over the true cosmological power spectrum in any reasonable observing scenario, and that only with very long observing times and removal of a large number of foreground sources can the true power spectrum be recovered.
The detection and characterization of the Stochastic Gravitational Wave Background (SGWB) is one of the main goals of Gravitational Wave (GW) experiments. The observed SGWB will be the combination of GWs from cosmological (as predicted by many models describing the physics of the early Universe) and astrophysical origins, which will arise from the superposition of GWs from unresolved sources whose signal is too faint to be detected. Therefore, it is important to have a proper modeling of the astrophysical SGWB (ASGWB) in order to disentangle the two signals; moreover, this will provide additional information on astrophysical properties of compact objects. Applying the Cosmic Rulers formalism, we compute the observed ASGWB angular power spectrum, hence using gauge invariant quantities, accounting for all effects intervening between the source and the observer. These are the so-called projection effects, which include Kaiser, Doppler and gravitational potentials effect. Our results show that these projection effects are the most important at the largest scales, and they contribute to up to tens of percent of the angular power spectrum amplitude, with the Kaiser term being the largest at all scales. While the exact impact of these results will depend on instrumental and astrophysical details, a precise theoretical modeling of the ASGWB will necessarily need to include all these projection effects.
We use population inference to explore the impact that uncertainties in the distribution of binary black holes (BBH) have on the astrophysical gravitational-wave background (AGWB). Our results show that the AGWB monopole is sensitive to the nature of the BBH population (particularly the local merger rate), while the anisotropic $C_ell$ spectrum is only modified to within a few percent, at a level which is insignificant compared to other sources of uncertainty (such as cosmic variance). This is very promising news for future observational studies of the AGWB, as it shows that (i) the monopole can be used as a new probe of the population of compact objects throughout cosmic history, complementary to direct observations by LIGO and Virgo and (ii) we are able to make surprisingly robust predictions for the $C_ell$ spectrum, even with only very approximate knowledge of the black hole population. As a result, the AGWB anisotropies have enormous potential as a new probe of the large-scale structure of the Universe, and of late-Universe cosmology in general.
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