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

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 σ 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 − α 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 ) = γ ± β r ± r 1 / 2 and all these models are found to be compatible with the ACT data.