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

TL;DR

This paper explores a non-minimally coupled squared-Quartic Hilltop inflation model in light of ACT and other observational data, deriving analytic expressions and showing compatibility with current constraints.

Contribution

It introduces a detailed analysis of the squared-Quartic Hilltop inflation potential with non-minimal coupling, providing analytic formulas and demonstrating consistency with recent cosmological observations.

Findings

Weak coupling regime slightly increases n_s and suppresses r, matching Planck-ACT-DESI constraints.

Strong coupling regime yields a flat potential plateau, with n_s around 0.9743 and r below 5×10^{-4}, compatible with ACT and BK18.

Inflation energy scale remains high, around 10^{-3} to 10^{-2} M_p, consistent with high-scale inflation scenarios.

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 \( V(\phi) = V_0 [1 - \lambda (\phi/M_p)^4]^2 \) 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 \( \lambda = 10^{-3}, \xi = 10^{-3}, {\cal N} = 117 \), values which are in agreement with the joint Planck--ACT--DESI (P-ACT-LB) constraints. On the other hand, for a strong coupled (\( \xi \gg 1 \)), 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 \( {\cal N} = 65{-}70 \), 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.