Noether symmetry for Gauss-Bonnet dilatonic gravity

TL;DR

This paper explores Noether symmetry in Gauss-Bonnet-Dilatonic gravity, revealing its persistence across cosmic eras and its role in explaining late-time acceleration without fine-tuning.

Contribution

It demonstrates the existence of Noether symmetry with specific potential and coupling forms in Gauss-Bonnet-Dilatonic gravity across different cosmological epochs.

Findings

Symmetry exists in vacuum, radiation, and matter eras.

Late-time acceleration driven by effective cosmological constant.

Gauss-Bonnet term offsets large cosmological constant value.

Abstract

Noether symmetry for Gauss-Bonnet-Dilatonic interaction exists for a constant dilatonic scalar potential and a linear functional dependence of the coupling parameter on the scalar field. The symmetry with the same form of the potential and coupling parameter exists all in the vacuum, radiation and matter dominated era. The late time acceleration is driven by the effective cos- mological constant rather than the Gauss-Bonnet term, while the later compensates for the large value of the effective cosmological constant giving a plausible answer to the well-known coincidence problem.