Implications of the scalar tilt for the tensor-to-scalar ratio

We investigate the possible implications of the measured value of the scalar tilt n(s) for the tensor-to-scalar ratio r in slow-roll, single-field inflationary models. The measured value of the tilt satisfies n(s) - 1 similar to 1/N-*, where N-* similar to 60 is the number of e-folds for observationally relevant scales. If this is not a coincidence and the scaling holds for different values of N, it strongly suggests that either r is as big as 10(-1) (a possibility in tension with the recent data), or smaller than 10(-2) and exponentially dependent on ns. A large region of the (ns,r) plane is not compatible with this scaling.