  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.
