Can CMB data constrain the inflationary field range?

TL;DR

This paper investigates how well the spectral index and tensor-to-scalar ratio constrain the inflationary field range, revealing degeneracies and an upper bound, with implications for models beyond slow-roll single-field inflation.

Contribution

It demonstrates that the inflationary field range is not uniquely determined by observable parameters and identifies an upper bound across various inflationary models.

Findings

Field range not uniquely determined by (n_s, r)

Existence of an upper bound on elta

Sub-Planckian elta possible beyond slow-roll

Abstract

We study to what extent the spectral index $n_s$ and the tensor-to-scalar ratio $r$ determine the field excursion $\Delta\phi$ during inflation. We analyse the possible degeneracy of $\Delta \phi$ by comparing three broad classes of inflationary models, with different dependence on the number of e-foldings $N$, to benchmark models of chaotic inflation with monomial potentials. The classes discussed cover a large set of inflationary single field models. We find that the field range is not uniquely determined for any value of $(n_s, r)$; one can have the same predictions as chaotic inflation and a very different $\Delta \phi$. Intriguingly, we find that the field range cannot exceed an upper bound that appears in different classes of models. Finally, $\Delta \phi$ can even become sub-Planckian, but this requires to go beyond the single-field slow-roll paradigm.