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

Abstract: 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(φ) = V_0 [1 - λ(φ/M_p)^4]^2 ) within the Einstein and Jordan frames. In the Jordan frame we introduce the coupling term ( ξφ^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 (( ξ\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 ( λ= 10^{-3}, ξ= 10^{-3}, {\cal 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 (( ξ\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 ( {\cal N} = 65{-}70 ), consistent with ACT and BK18 bounds. The associated energy scale of inflation, ( V_0^{1/4} \sim 10^{-3}{-}10^{-2} M_p ), remains compatible with high-scale inflationary scenarios.