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For the monomial inflation potential on $\varphi >0$, $V_{,\varphi }/V=n/\varphi$ and $V_{,\varphi \varphi }/V=n(n-1)/{\varphi }^2$. Thus, to leading slow-roll approximation,For $n=2,3,4$, $2n\ge n^2/2$. Therefore the loose order-one requirements $ϵ\le 1$ and $|\eta |\le 1$ giveThis is the interpretation under which the printed threshold follows. It is not a sufficient criterion for genuine slow roll, which requires much smaller parameters and hence ${\varphi }^2/M_{\mathrm{Pl}}^2\gg 2n$ for these fixed powers. Nor is its equality the actual end of acceleration for $n=2,3$: there $ϵ\simeq n/4<1$. For $n=4$ the leading estimate has $ϵ\simeq 1$. The potential-based order-one criterion $|{\eta }_V|<1$ also differs from the Hubble-flow criterion, especially at $n=4$. We use the endpoint the paper explicitly stipulates, rather than treating this boundary as a controlled slow-roll approximation.

Let ${\varphi }_e^2=2n{M}_{\mathrm{Pl}}^2$ by that prescription. The slow-roll e-fold count, using $\dot{\varphi }/H\simeq -n{M}_{\mathrm{Pl}}^2/\varphi$, isFor $N=60$, the monomial inflation with a prescribed endpoint result isApplying the leading scalar spectral index in Hubble slow-roll parameters and tensor-to-scalar ratio formulas givesThese are predictions at the chosen 60-e-fold initial point, normally identified with the pivot scale's horizon exit. A physical endpoint determined by $ϵ=1$ would instead have the leading estimate ${\varphi }_e^2\simeq n^2{M}_{\mathrm{Pl}}^2/2$; its change to the e-fold count and predictions must not be silently mixed with the stipulated $122n$ calculation.