Constraining $β$-Exponential Inflation with the latest ACT observations

Abstract: Recent observations from the Atacama Cosmology Telescope (ACT), especially when combined with DESI baryon acoustic oscillation data, indicate a scalar spectral index $n_s$ higher than the value reported by \textit{Planck} 2018, placing tension on universal inflationary attractor models. Motivated by this discrepancy, we investigate the inflationary predictions of the $β$-exponential potential, $V(φ)=V_0\left(1-λβφ/M_p\right)^{1/β}$ considering both minimally and non-minimally coupled realizations. This potential generalizes standard exponential inflation and naturally arises in braneworld scenarios. We derive analytical expressions for the slow-roll parameters and inflationary observables using a perturbative expansion in the non-minimal coupling $ξ$, and validate these results through numerical calculations. In the minimally coupled case, the model predicts $n_s \simeq 0.976$ and $r \simeq 0.035$ for $N=50$ and moderate values of β, remaining compatible with ACT+DESI constraints at the 1σlevel while yielding a spectral tilt larger than the universal attractor prediction. Introducing a small non-minimal coupling significantly improves agreement with observations by suppressing the tensor-to-scalar ratio while preserving the enhanced scalar tilt. For $N=60, λ\sim 0.3-0.5$, and $β\sim O(1-5)$, the non-minimally coupled model yields $n_s \simeq 0.974-0.976$ and $r \lesssim 0.03$, comfortably consistent with ACT, DESI, and BICEP/Keck bounds. Our results show that the $β$-exponential potential, especially when implemented with a non-minimal coupling, exhibits good agreement with the latest CMB observations. Our inflationary predictions of the non-minimal model of $n_s$ and $r$ confirming the leading-order contributions in $ξ$ are sufficient to capture the essential features of both $r$ and $n_s$ in observationally relevant regimes.