  Characterizing the physical properties of the stochastic gravitational waves
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
non-trivial 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 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.
