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

TL;DR

This paper explores how the measured scalar tilt in inflationary models constrains the tensor-to-scalar ratio, suggesting it is either relatively large or exponentially small, with many parameter regions being incompatible.

Contribution

It demonstrates a scaling relation between scalar tilt and tensor-to-scalar ratio that constrains inflationary model parameters.

Findings

If the tilt scaling holds, r is either around 0.1 or less than 0.01.

A large part of the (n_s, r) parameter space is incompatible with this scaling.

The relation links the scalar tilt to the tensor-to-scalar ratio in a way that impacts inflationary model viability.

Abstract

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.