Description
While the power spectrum of the stochastic gravitational wave background (SGWB) characterizes the energy density of the background, the three-point function (bispectrum) encodes the dynamics of interactions. In this talk, we focus on the squeezed limit of the tensor bispectrum, where one mode is significantly longer than the other two. First, we review the theoretical connection between gravitational soft theorems and the squeezed bispectrum in flat spacetime, drawing a parallel to their well-known cosmological counterpart: the consistency relation in the tensor sector. Second, we propose a multi-frequency observational strategy to search for this signal. By leveraging the vast scale separation between Pulsar Timing Arrays ( ~nano Hz) and space-based interferometers like LISA (~0.001 Hz ), we construct a cross-correlation statistic that treats the PTA residuals as a background field modulating the power of the short modes observed by LISA.
