Multimessenger cosmology: Correlating cosmic microwave background and stochastic gravitational wave background measurements

Characterizing the physical properties of the stochastic gravitational wave background (SGWB) is a key step towards identifying the nature of its possible origin. We focus our analysis on SGWB anisotropies. The existence of a nontrivial primordial scalar-tensor-tensor (STT) correlation in the squeezed configuration may be inferred from the effect that a long wavelength scalar mode has on the gravitational wave power spectrum: an anisotropic contribution. Crucially, such a contribution is correlated with temperature anisotropies in the cosmic microwave background (CMB). We show that, for inflationary models that generate suitably large STT non-Gaussianities, cross correlating the CMB with the stochastic background of gravitational waves is a very effective probe of early universe physics. The resulting signal can be a smoking gun for primordial SGWB anisotropies.

Figure 1

Cross correlation of the GW anisotropy with the CMB in the Sachs-Wolfe limit. The correlation decays exponentially with a characteristic scale ${\ell }_{*}\approx 44$.

Figure 2

Top: $\sigma$-sourced contributions to the scalar (A) and tensor (B) power spectra. Bottom: main contribution to $⟨\zeta \gamma \gamma ⟩$. The solid line stands for $\zeta$ propagators, wiggly lines are for $\gamma$, dashed lines are for $\sigma$. The bispectrum diagram at the bottom relies on the $\mu {\sigma }^3$ interaction in the cubic Lagrangian [see 3rd line of Eq. (18)] for the vertex. It builds instead on the ${\sigma }_0\pi$ and ${\sigma }_2\gamma$ mixing in the quadratic Lagrangian [1st line of Eq. (18)] to contract external legs with internal ones.