Reconstructing inflation in Einstein-Gauss-Bonnet gravity in light of ACT data

During the inflationary epoch, we investigate the reconstruction of the background variables within the framework of Einstein-Gauss-Bonnet gravity, considering the scalar spectral index $n_s(N)$ and the tensor-to-scalar ratio $r(N)$, where $N$ denotes the number of $e-$folds. Under a general formalism, we determine the effective potential and the coupling function associated with the Gauss-Bonnet term as functions of the cosmological parameters $n_s(N)$ and $r(N)$, respectively. To implement the reconstruction  methodology for the background variables, we study an example in which the attractors for the index $n_s$ and the ratio $r$ are in agreement with  Atacama Cosmology Telescope (ACT) data. In this context, explicit expressions for the effective potential $V(\phi)$ and the coupling parameter $\xi(\phi)$ are reconstructed. Moreover, the reconstruction based on  observational parameters shows that $V(\phi)\not\propto 1/\xi(\phi)$, in contrast to the assumption adopted in the literature for the study of the  evolution of the universe in Einstein-Gauss-Bonnet gravity.