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 $\Delta\phi$ 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.