Approximate reconstruction of inflationary potential with ACT observations

The Atacama Cosmology Telescope (ACT) has recently reported updated measurements of the scalar spectral index n s , revealing a tension with the predictions of many conventional inflationary models. In this work, we adopt a parameterization of the spectral index in the form n s = 1 − p / ( N + α ) with 1.338 < p < 1.746, to reconstruct an inflationary potential consistent with the latest ACT data. The resulting potential is the Kachru–Kallosh–Linde–Trivedi (KKLT) potential V ( ϕ ) = V 0 / [ 1 + ( M / ϕ ) n ] , where the power index is given by n = 2 ( p − 1 ) / ( 2 − p ) . The corresponding tensor-to-scalar ratio is approximately r ≈ 16 ( p − 1 ) / [ C ( N + α ) p ] with C = 2 2 p − 1 [ p − 1 / ( 2 − p ) ] 2 p − 2 / M 2 p − 2 . Since the reconstruction under the slow-roll approximation is model-independent, the KKLT model can serve as an effective approximation to a broad class of inflationary scenarios that are consistent with the latest ACT measurements of n s , at least on large scales.