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 $n_s -1\sim 1/N_*$, where $N_* \sim 60$ 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 $n_s$. A large region of the ($n_s$,$r$) plane is not compatible with this scaling.

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