Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
Guido Cognola, Emilio Elizalde, Shin'ichi Nojiri, Sergei D. Odintsov, Sergio Zerbini
TL;DR
The paper demonstrates that modifying gravity with functions of the Gauss-Bonnet invariant, particularly through F(G,R) and its special case F(G,R) = R/(2κ^2) + f(G), can naturally reproduce late-time cosmic acceleration as effective dark energy (cosmological constant, quintessence, or phantom) while preserving Solar System tests. It analyzes the FRW dynamics, identifies de Sitter and SdS solutions, and computes horizon entropy via Wald’s method, showing the framework’s consistency with gravitational thermodynamics. A one-loop quantization on de Sitter space suggests a viable quantum treatment akin to F(R) gravity, and the model supports a transition from deceleration to acceleration, offering a unified route to inflation and late-time acceleration. Furthermore, the authors explore potential resolutions to the hierarchy problem within scalar-tensor and F(G,R) extensions, illustrating how a time-dependent effective gravitational coupling can bring Planck-scale physics into the weak scale. Collectively, the work indicates modified GB gravity as a flexible, testable platform for addressing both cosmological acceleration and fundamental scale hierarchies, with clear directions for observational and perturbative investigations.
Abstract
Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, $f(G)$, is added to the General Relativity action. We show that such theory is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence or phantom cosmic acceleration, with a possible transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with Solar System constraints. Specific properties of $f(G)$ gravity in a de Sitter universe, such as dS and SdS solutions, their entropy and its explicit one-loop quantization are studied. The issue of a possible solution of the hierarchy problem in modified gravities is addressed too.