Constraining β-exponential inflation with the latest ACT observations

Recent observations from the Atacama Cosmology Telescope (ACT), especially when combined with DESI baryon acoustic oscillation data, indicate a scalar spectral index nₛ n s higher than the value reported by Planck 2018, placing tension on universal inflationary attractor models. Motivated by this discrepancy, we investigate the inflationary predictions of the β β -exponential potential, V(φ )=V₀( 1-λ β φ /Mₚ) 1/β V ( ϕ ) = V 0 1 - λ β ϕ / M p 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 ξ , and validate these results through numerical calculations. In the minimally coupled case, the model predicts nₛ 0.976 n s ≃ 0.976 and r 0.035 r ≃ 0.035 for $$N=50$$ N = 50 and moderate values of β β , remaining compatible with ACT+DESI (P-ACT-LB) constraints at the 1σ 1 σ 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 $$N=60 $$ N = 60 , λ ~ 0.3\!-\!0.5 λ ∼ 0.3 - 0.5 , and β ~ O(1\!-\!5) β ∼ O ( 1 - 5 ) , the non-minimally coupled model yields $$ n_s \