Constraining non-minimally coupled squared-Quartic Hilltop Inflation in light of ACT observations

The combination of the data from the Dark Energy Spectroscopic Instrument (DESI) with the recent measurements from the Atacama Cosmology Telescope (ACT) indicate that the scalar spectral index $n_s$ has a larger value than the Planck 2018 which leads to tension within standard inflationary models. In this study in order to explain the new data, We consider the squared-Quartic Hilltop inflation potential $V(\phi )=V_0[1-\lambda (\phi \mathrm{/}{M}_p{)}^4{]}^2$ within the Einstein and Jordan frames. In the Jordan frame we introduce the coupling term $\xi {\phi }^{2}R$ and we calculate analytic expressions for the slow-roll parameters, scalar spectral index, and tensor-to-scalar ratio on the weak and strong coupling regimes. In the weak limit ($\xi \ll 1$), perturbative corrections slightly increase $n_s$ and suppress $r$, leading to $n_s\simeq 0.9743$ and $r\sim 7.8\times {10}^{-5}$ for representative parameters $\lambda ={10}^{-3},\xi ={10}^{-3},\mathcal{N}=117$, values which are in agreement with the joint Planck–ACT–DESI (P-ACT-LB) constraints. On the other hand, for a strong coupled ($\xi \gg 1$), the conformal rescaling provides an exponentially flat potential plateau, which allows us to calculate $n_s\approx 0.9743$ with $r\lesssim 5\times {10}^{-4}$ for $\mathcal{N}=65-70$, consistent with ACT and BK18 bounds. The associated energy scale of inflation, $V_0^{1\mathrm{/}4}\sim {10}^{-3}-{10}^{-2}{M}_p$, remains compatible with high-scale inflationary scenarios.