Universality of Primordial Anisotropies in Gravitational Wave Background

Abstract

We propose a model-independent formalism for describing anisotropies in the stochastic gravitational wave background (SGWB) originating from primordial perturbations. Despite their diverse physical origins -- such as Sachs-Wolfe effects, integrated Sachs-Wolfe effects, or fossil effects from primordial non-Gaussianity -- SGWB anisotropies exhibit a universal angular structure. We show that this universality arises from a single vertex function, the Cosmological Form Factor (CFF), which encodes the information on how long-wavelength modes modulate the SGWB statistics. Two fundamental principles -- statistical isotropy and locality -- uniquely determine the angular dependence of the CFF, resulting in a universal multipole scaling of the SGWB anisotropies. The CFF formalism provides a common language for classifying SGWB anisotropies and offers a powerful framework for interpreting upcoming observations.

Figures (2)

• Figure 1: Schematic illustration of the origin of SGWB anisotropies from long-wavelength perturbations. Gravitational waves observed in directions $\hat{\boldsymbol{q}}$ and $\hat{\boldsymbol{q}}’$ experience different local environments due to the presence of a long mode $\phi(\boldsymbol{k}_L)$, resulting in statistical anisotropies.
• Figure 2: Diagrammatic interpretation for the computation of the angular power spectrum \ref{['eq:Clgw']} mediated by a single long mode. The CFF, $F(\boldsymbol{q}, \boldsymbol{k}_L)$, is represented by the vertices (circles) between the GW anisotropies $\delta_\text{GW}$ (double wavy lines) and the long modes $\phi_L$ (solid lines).