Constraining $\beta$-Exponential Inflation with the latest ACT observations

TL;DR

This paper investigates the $eta$-exponential inflationary model, especially with non-minimal coupling, demonstrating its compatibility with recent ACT, DESI, and BICEP/Keck CMB observations by deriving analytical and numerical predictions for spectral index and tensor-to-scalar ratio.

Contribution

It provides analytical expressions and numerical validation for the $eta$-exponential inflation model with non-minimal coupling, showing improved observational agreement over standard models.

Findings

Minimally coupled model predicts $n_s \,\approx\, 0.976$ and $r \,\approx\, 0.035 for $N=50$.

Non-minimal coupling suppresses $r$ and maintains $n_s$ within observational bounds.

Model with non-minimal coupling is consistent with ACT, DESI, and BICEP/Keck data.

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 $\beta$-exponential potential, $V(\phi)=V_0\left(1-\lambda\beta\phi/M_p\right)^{1/\beta}$ 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 $\xi$, 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 \beta, remaining compatible with ACT+DESI constraints at the 1\sigma level 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 $N=60, \lambda \sim 0.3-0.5$, and $\beta \sim O(1-5)$, 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 $\beta$-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 $\xi$ are sufficient to capture the essential features of both $r$ and $n_s$ in observationally relevant regimes.