Potential Reconstruction from ACT Observations Leading to Polynomial α-Attractor

The Atacama Cosmology Telescope (ACT) has recently reported updated measurements of the scalar spectral index nₛ, which exhibit tension with predictions from many conventional inflationary models when combined with other observational data. In this work, we adopt a parameterization of the spectral index of the form nₛ = 1 - p/(N + α) and reconstruct an inflationary potential that is consistent with the latest ACT data. The resulting potential takes the form of an inverse-power plateau, V(φ)=V₀[1-(M/φ)ⁿ], where the power index is given $n = 2(p-1)/(2-p)$. To match ACT constraints, n can be chosen as $1$, $2$, $3$, $4$, or $5$. The corresponding tensor-to-scalar ratio is r ≈ 16(p-1)/[C (N+α)ᵖ] with C= 2²ᵖ⁻¹ [√p-1/(2-p)]²ᵖ⁻² /M²ᵖ⁻². The reconstructed potential corresponds to the form of the Polynomial α-attractor potential. Since the reconstruction is model-independent, any inflationary model yielding predictions of the form nₛ = 1 - p/(N + α) and satisfying observational constraints will exhibit a potential profile at the slow-roll region closely resembling that of the Polynomial α-attractor.