Characterizing the cosmological gravitational wave background: Anisotropies and non-Gaussianity

Abstract

A future detection of the stochastic gravitational wave background (SGWB) with gravitational wave (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 nonlinear 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 that found in the literature for the case of cosmic microwave background perturbations.

Deformation of the gravitational wave spectrum by density perturbations

“…In close analogy to the analysis of CMB photons, we can now ♦4 See Refs. [7][8][9][10][11][12][13] for related analysis of the anisotropies of the SGWB. ♦5 For inflationary GWs, we take "source time" labeled by "s" to be when the relevant GWs are well inside the horizon.…”

“…♦ 13 One may wonder why the amplitude decreases (∆lnA)SW = Ψo − Ψs < 0 when the GW escapes from a positive Newtonian potential Φs = Ψs > 0 to the observer's position Φo = Ψo = 0. Here, we have to be careful about the normalization condition of the polarization tensor eµν e µν = eije ij = 1, which gives eij ∝ 1 − 2Ψ in our setup (here we assumed the gauge condition hµ0 = 0).…”

“…in [6]. For the stochastic background, these effects have been shown to modify and generate anisotropic contributions of the SGWB [7][8][9][10][11][12][13][14] and to lead to a decoherence of the phase information in the SGWB which becomes relevant when probing the three-point function of GWs [15,16]. ♦1 Here, given the limited angular resolution of GW detectors, we instead focus on the isotropic component of the GW power spectrum.…”

“…GW power spectrum 2 h is approximately flat. This will be particularly relevant for future GW detectors such as LISA [13], the Einstein Telescope [14] of DECIGO [15], which will be able to measure the SGWB with high accuracy.…”

Primordial non-Gaussianity in supersolid inflation

“…A considerable effort is devoted to search for signatures of inflation by studying the CMB and the large scale structure of the Universe. The progress in detecting GWs and the forthcoming space interferometer LISA give new opportunities to test the physics of inflation, and more in general, the early Universe on scales very different from the ones of the CMB [39][40][41]. In this context, primordial non-gaussianity can be used to distinguish single clock inflation from multi-field models.…”