Reconstructing ACT-compatible and GW170817-compatible Einstein-Gauss-Bonnet Inflation from the Observational Indices

In this work we use an inverse reconstruction technique for constructing ACT-compatible and GW170817-compatible Einstein-Gauss-Bonnet inflationary theories. From a given tensor-to-scalar ratio using the reconstruction technique, we find which scalar Gauss-Bonnet coupling function and which scalar potential can yield the given tensor-to-scalar ratio. We present the formalism and the viable theories pass a series of observational tests, including the amplitude of the scalar perturbations, which is non-trivial for Einstein-Gauss-Bonnet theories. We present four viable models of inflation that pass all the observational tests.