Approximate reconstruction of inflationary potential with ACT observations

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 $n_s=1-p/(N+\alpha )$ 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 $V(\varphi )=V_0/[1+(M/\varphi {)}^n]$, 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.

11 pages, 3 figures, accepted for publication in PLB

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• Inflationary attractors and radiative corrections in light of ACT data
• Harrison-Zeldovich attractor: From Planck to ACT results
• Induced-Gravity Palatini-Like Higgs Inflation in Supergravity Confronts ACT DR6
• Reconciling the ACT Preference in $f(T)$ Gravity: Inflation and Reheating Constraints
• Constraints on non-canonical chaotic inflation from ACT DR6 and BICEP/Keck data
• Mutated hilltop inflation in light of Planck/ACT observations