Unifying inflation with early and late dark energy in Einstein-Gauss-Bonnet gravity

In the era of precision cosmology, different observational data has led to precise measurements of the Hubble constant that differ significantly, what has been called the Hubble tension problem. In order to solve such a discrepancy, many different solutions have been proposed, from systematic errors on the observational data to theoretical proposals that assume an early dark energy that might affect the universe expansion at the time of recombination. In this paper, a model of varying cosmological constant is proposed in the framework of Einstein-Gauss-Bonnet gravity. The corresponding gravitational action is reconstructed and such a model is shown to reproduce well the inflationary era together with dark energy epoch and at the same time to provide an explanation for the discrepancy on the Hubble constant predictions. The transition to a phantom epoch is also realized, avoiding the usual instability problems of ordinary scalar field models.