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

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.