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Derive both cases from $V=C_p(\Phi /M_{\mathrm{Pl}}{)}^p$, using the positive-field branch. The potential slow-roll parameter and second potential slow-roll parameter areTaking the leading inflation-end estimate ${ϵ}_V=1$, the remaining number of e-folds isThe corresponding monomial-inflation curvature amplitude and tilt areIn particular,The quartic case is redder. Its small-$k$ matter envelope is $k^{0.9508}$ instead of $k^{0.9669}$; its high-$k$ envelope is $k^{-3.0492}{\ln }^{2}k$ instead of $k^{-3.0331}{\ln }^{2}k$. With the late cosmology fixed, the turnover and baryonic acoustic scale do not move. If the spectra are matched in amplitude at a pivot $k_{\ast }$, their ratio is approximatelyThis gives more large-scale power and less small-scale power relative to the pivot, with about a $7\%$ relative tilt across two decades in wavenumber.

The quartic coefficient is not specified, so changing the power of the potential does not by itself specify the overall amplitude. If $C_2=V_0$ and the quartic coefficient is $C_4$, the formula above gives, at the same $N$,Consequently choosing the same dimensionful coefficient would give a very different normalization, whereas choosing $C_4/V_0\simeq 1/496$ matches the pivot amplitude. These are different normalization choices, not a universal amplitude prediction from a quartic shape alone.