Gravitational Wave Direct Detection does not Constrain the Tensor Spectral Index at CMB Scales

I discuss constraints on the power spectrum of primordial tensor perturbations from a combination of Cosmic Microwave Background (CMB) measurements and the gravitational wave direct detection experiments LIGO/Virgo and DECIGO. There are two main points: (1) Inflation predicts an approximately power-law form for the primordial tensor spectrum, but makes no prediction for its amplitude. Given that neither Planck nor LIGO/Virgo has actually detected primordial tensor modes, it is trivially true that no model-independent constraint on the slope of the tensor power spectrum is possible with current data. (2) CMB and LIGO/Virgo scales differ by more than 19 orders of magnitude, and 16 for DECIGO. I show that a power-law extrapolation from CMB to direct detection frequencies overestimates the amplitude of primordial tensor modes by as much as two orders of magnitude relative to an ensemble of realistic single-field inflation models. Moreover, the primordial tensor amplitude at direct detection scales is mostly uncorrelated with the tensor spectral index at CMB scales, and any constraint is strongly dependent on the specific form of the inflationary potential.