 Quadratic-inflation field interval from a wavenumber interval

For a quadratic inflaton potential ending at the leading estimate ${ϵ}_V=1$, $\Phi /M_{\mathrm{Pl}}=\sqrt{4N+2}$. Cosmological horizon exit gives $d\log k/dN=-1+{ϵ}_H$. A narrow logarithmic interval therefore probes a field span $2\Delta \log k/(\sqrt{4N+2}(1-{ϵ}_H))$, to the accuracy of the slow-roll approximation. At sixty e-folds, five logarithmic wavenumber units probe about $0.64M_{\mathrm{Pl}}$ around a background field near $15.6M_{\mathrm{Pl}}$.