Can CMB data constrain the inflationary field range?

Abstract

We study to what extent the spectral index $n_s$ and the tensor-to-scalar ratio $r$ determine the field excursion $\Delta \varphi$ during inflation. We analyse the possible degeneracy of $\Delta \varphi$ 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 $\Delta \varphi$. Intriguingly, we find that the field range cannot exceed an upper bound that appears in different classes of models. Finally, $\Delta \varphi$ can even become sub-Planckian, but this requires to go beyond the single-field slow-roll paradigm.

Comments: 15 pages, 7 figures. v2: minor typos corrected, refs added, JCAP version