General Scalar Field Inflation ACT Attractors: Utilizing the $n_s(r)$ relation

TL;DR

This paper develops new single scalar field inflation models with specific $n_s(r)$ relations, finding three classes of potentials compatible with ACT data, expanding the landscape of viable inflationary scenarios.

Contribution

It introduces a top-down method to derive inflationary potentials from desired $n_s(r)$ relations, including variants of known attractor models, compatible with ACT observations.

Findings

Discovered three classes of potentials fitting ACT data

Established analytical relations between $n_s(r)$ and inflationary potentials

Extended the family of inflation models beyond known attractors

Abstract

The ACT data have severely constrained the single scalar field models. Known models of inflation, like the Starobinsky model, the Higgs model and the $a$-attractors are at least $2\sigma$ off the ACT data. In this work we aim to provide a top-to-bottom approach in single scalar field inflationary cosmology compatible with the ACT data. Specifically, inspired by the fact that the Starobinsky model, the Higgs model and the $a$-attractors, all being plateau potentials, result to the same attractor relation between the spectral index of scalar perturbations and the tensor-to-scalar ratio, which is of the form $n_s(r)=1-\alpha r^{1/2}$, in this work we seek for attractors of the form $n_s(r)=f(r)$ that may lead to ACT-compatible inflation. Specifically, we fix the function $f(r)$ to have a specific desirable form and then solve the differential equation $n_s(r)=f(r)$ to find the potential which results to the relation $n_s(r)=f(r)$. We discovered analytically three classes of potentials which are variants of the general form $n_s(r)=\gamma \pm \beta r \pm r^{1/2}$ and all these models are found to be compatible with the ACT data.