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

TL;DR

The paper addresses the tension between ACT-DESI and Planck regarding the scalar spectral index $n_s$ by exploring a squared-Quartic Hilltop potential with possible non-minimal coupling to gravity. It develops analytic slow-roll expressions in both Einstein and Jordan frames and analyzes weak and strong coupling regimes, finding that in the weak-coupling limit $n_s oughly 0.974$ and $r$ can be as small as $7.8\times10^{-5}$, while in the strong-coupling regime a plateau yields $n_s \approx 0.974$ with $r \lesssim 5\times10^{-4}$ for $N\approx65$–70; both regimes are compatible with ACT and BK18 constraints. The inflation scale remains $V_0^{1/4} \sim 10^{-3}-10^{-2} M_p$, keeping high-scale inflation viable. The results demonstrate that non-minimal coupling provides a flexible path to fit updated CMB constraints and motivate future work on radiative corrections, reheating, and swampland considerations.

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.

Figures (2)

• Figure 1: Constraints on the scalar and tensor primordial power spectra, shown in the $r-n_{s}$ parameter space predicted by the nonminimally-coupled model for a weakly coupled case ($\xi \ll 1$). Left panel: ${\cal N}=[65,\,85,\,115]$ are kept fixed, while varying $\lambda$; Right panel: we choose $\lambda=10^{-3}$ and $\lambda=10^{-4}$ and fix a parameter $\xi=10^{-3}$, while varying $\cal N$. The bounds on $r$ are primarily determined by the BK18 observations, whereas the limits on $n_s$ are set by Planck (red) and P-ACT (green) data.
• Figure 2: Constraints on the scalar and tensor primordial power spectra, shown in the $r-n_{s}$ parameter space predicted by the nonminimally-coupled model for a strongly coupled case ($\xi \gg 1$). ${\cal N}=[60,\,65,\,70]$ are kept fixed, while varying $\lambda=[10^{-4},\,10^{-3}]$. The bounds on $r$ are primarily determined by the BK18 observations, whereas the limits on $n_s$ are set by Planck (red) and P-ACT (green) data.