Can CMB data constrain the inflationary field range?

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

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