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

TL;DR

This paper reconstructs the inflationary potential and Gauss-Bonnet coupling in Einstein-Gauss-Bonnet gravity using ACT observational data, providing explicit models consistent with current cosmological measurements.

Contribution

It introduces a reconstruction method for inflationary variables in Einstein-Gauss-Bonnet gravity based on ACT data, revealing new relations between potential and coupling functions.

Findings

Reconstructed explicit forms of $V()$ and $\xi()$ consistent with ACT data.

Found that $V()$ is not proportional to $1/\xi()$, challenging previous assumptions.

Demonstrated the viability of Einstein-Gauss-Bonnet inflation models with observational constraints.

Abstract

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.