Probing Early Universe Physics with Gravitational-Wave Correlators

This research delves into the non-Gaussian features of stochastic gravitational-wave backgrounds (SGWBs) to explore early-Universe physics and potential dark-sector dynamics. By focusing on higher-order correlators, particularly the four-point functions that generate a connected contribution to the GW trispectrum, the study aims to extract additional information beyond the standard GW power spectrum. The SGWBs are generated at second order by vector fluctuations, a class of sources motivated by early-Universe scenarios.

The study develops tools to characterize these higher-order GW correlators and computes representative four-point functions. The results show that the trispectrum amplitude scales as the square of the GW power spectrum and peaks in characteristic folded momentum configurations, reflecting the structure of the nonlinear source. The observational implications are explored by demonstrating the contribution of the connected trispectrum to the variance of two-point overlap reduction functions and constructing an optimal estimator to measure the connected trispectrum with ground-based interferometers. This work highlights the potential of non-Gaussian SGWB statistics to provide a complementary observable for probing the origin of GW backgrounds and distinguishing cosmological from astrophysical sources.

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