Gauss–Bonnet Theory and Applications in Cosmology

Abstract

This review provides a comprehensive discussion of Gauss–Bonnet (GB) gravity, a gravitational theory incorporating higher-order curvature corrections, which can influence gravitational dynamics in higher dimensions. We explore the fundamental motivation for introducing the GB term, particularly in the context of high-energy physics and string theory-inspired scenarios, highlighting its potential in addressing key issues such as singularities, the nature of dark energy, cosmic acceleration, modifications to neutron stars and black holes, and cosmological singularities. Furthermore, we examine emerging research directions and recent advancements in the field, including torsion effects, compact astrophysical phenomena, and modified Gauss–Bonnet models, which further expand the applications of GB gravity in modern theoretical physics and cosmology.