Constraining $$\beta $$-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 $$ n_s $$ 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 $$\beta $$ β -exponential potential, $$ V(\phi )=V_0\left( 1-\lambda \beta \phi /M_p\right) ^{1/\beta }$$ 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 $$\xi $$ ξ , and validate these results through numerical calculations. In the minimally coupled case, the model predicts $$ n_s \simeq 0.976 $$ n s ≃ 0.976 and $$ r \simeq 0.035 $$ r ≃ 0.035 for $$N=50$$ N = 50 and moderate values of $$\beta $$ β , remaining compatible with ACT+DESI (P-ACT-LB) constraints at the $$1\sigma $$ 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 , $$ \lambda \sim 0.3\!-\!0.5 $$ λ ∼ 0.3 - 0.5 , and $$ \beta \sim \mathcal {O}(1\!-\!5) $$ β ∼ O ( 1 - 5 ) , the non-minimally coupled model yields $$ n_s \