Fossilized gravitational wave relic and primordial clocks

If long-wavelength primordial tensor modes are coupled to short-wavelength scalar modes, the scalar curvature two-point function will have an off-diagonal component. This fossil remnant is a signature of a mode coupling that cannot be achieved in single-clock inflation. Any constraint on its presence allows a cross-check of the relationship between the dynamical generation of the fluctuations and the evolution of the inflationary background. We use the example of non-Bunch-Davies initial states for the tensor and scalar modes to demonstrate that physically reasonable fossils, consistent with current data, can be observable in the near future. We illustrate how the fossil off-diagonal power spectrum is a complementary probe to the squeezed limit bispectra of the scalar and tensor sectors individually. We also quantify the relation between the observable signal and the squeezed limit bispectrum for a general scalar-scalar-fossil coupling and note the effect of superhorizon tensor modes on the anisotropy in scalar modes.