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 $n_s = 1 - p/(N + \alpha)$ 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 $V(\phi) = V_0/[1 + (M/\phi)^n]$, where the power index is given by $n = 2(p-1)/(2-p)$. The corresponding tensor-to-scalar ratio is approximately $r \approx 16(p-1)/[C (N+\alpha)^p]$ with $C= 2^{2p-1} \left[\sqrt{p-1}/(2-p)\right]^{2p-2} /M^{2p-2}$. 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.