Approximate reconstruction of inflationary potential with ACT observations
Zhu Yi, Xingzhi Wang, Qing Gao, Yungui Gong
Abstract
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.