Prospects for detecting anisotropies and polarization of the stochastic gravitational wave background with ground-based detectors

Abstract

We build an analytical framework to study the observability of anisotropies and a net chiral polarization of the Stochastic Gravitational Wave Background (SGWB) with a generic network of ground-based detectors. We apply this formalism to perform a Fisher forecast of the performance of a network consisting of the current interferometers (LIGO, Virgo and KAGRA) and planned third-generation ones, such as the Einstein Telescope and Cosmic Explorer. Our results yield limits on the observability of anisotropic modes, spanning across noise- and signal-dominated regimes. We find that if the isotropic component of the SGWB has an amplitude close to the current limit, third-generation interferometers with an observation time of 10 years can measure multipoles (in a spherical harmonic expansion) up to ℓ = 8 with 𝒪(10-3 – 10-2) accuracy relative to the isotropic component, and an 𝒪(10-3) amount of net polarization. For weaker signals, the accuracy worsens as roughly the inverse of the SGWB amplitude.

Observing gravitational waves with solar system astrometry

“…Using the fact that both cos(θ) and cos(2θ) average to 1/2, and setting the optimal filter Q(f ) in an analogous manner to what has been done in [28] we obtain…”

Science with the Einstein Telescope: a comparison of different designs

“…In this section we study the angular resolution of different ET configurations in the context of an SGWB. We follow the formalism in [117], whom we refer the reader for details and derivations (see also [118,119] for recent forecasts about the ET sensitivity to angular anisotropies). The sensitivity with which we can measure a given multipole of the background intensity is characterized by a quantity, N , such that the signal-to-noise ratio of an angular power spectrum is given by…”

GW_CLASS: Cosmological Gravitational Wave Background in the cosmic linear anisotropy solving system

“…we are computing the anisotropies of cosmological GW background that can be detected by current and future GW interferometers, thus the smallest frequencies considered are in the Pulsar Timing Array (PTA) band (around the nHz) and the angular scales that can be probed (typically up to a multipole ℓ max ≈ 10 − 15 [26,47]) are much larger than the wavelength of the GWs. Along each geodesic, GWs can be described by a distribution function f GW (x µ , p µ ), where x µ denotes position and p µ = dx µ /dλ momentum (which relates to the GW frequency).…”

“…For this purpose, we rely on previous investigations of CGWB anisotropy map reconstruction techniques [26,39,47,98,99,104]. The problem consists in finding optimal algorithms to go from raw data to CGWB maps at a given frequency.…”

“…It has been shown in the literature that mapping anisotropies in the SGWB [15][16][17][18] would provide a powerful way to distinguish between (different contributions to) the astrophysical background (generated by many overlapping or faint sources) [19][20][21][22][23][24][25] and the cosmological one [2][3][4] (see [26] for a recent forecast about detection of anisotropies with future groundbased detectors.). Like for CMB photons, the energy density of GWs exhibits small spatial fluctuations, which carry information both on the GW production mechanism and on the properties of the universe along each line of sight.…”