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

Giulia Cusin , Cyril Pitrou (1, 2) , Jean-Philippe Uzan (1, 2)

1 Institut Lagrange de Paris
2 IAP - Institut d'Astrophysique de Paris

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 understanding 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.

Mots clés: gravitational radiation: background; power spectrum: angular dependence; gravitational radiation: stochastic; gravitational radiation: energy; background: stochastic; energy: density; correlation function; space-time; cosmic background radiation; gravitational radiation; cosmic background radiation: anisotropy; cosmic background radiation: power spectrum; galaxy; cosmological model; gravitation: lens; mathematical methods; numerical calculations; space-time: Robertson-Walker

Domaines: Astrophysique [astro-ph]; Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Giulia Cusin, Cyril Pitrou, Jean-Philippe Uzan. Anisotropy of the astrophysical gravitational wave background: Analytic expression of the angular power spectrum and correlation with cosmological observations. Physical Review D, 2017, 96 (10), pp.103019. ⟨10.1103/PhysRevD.96.103019⟩. ⟨hal-01669773⟩