Field Equations in Chern-Simons-Gauss-Bonnet Gravity

TL;DR

This paper derives the complete set of field equations for Chern-Simons-Gauss-Bonnet gravity, enabling numerical solutions and observational constraints for various fundamental metrics, integrating scalar fields from string theory and parity violation.

Contribution

It provides the full set of equations of motion for Chern-Simons-Gauss-Bonnet gravity applied to key metrics without prior assumptions, facilitating future numerical and observational studies.

Findings

Complete set of field equations derived

Applicable to multiple fundamental metrics

Framework for numerical solutions and constraints

Abstract

We investigate the effects of Chern-Simons-Gauss-Bonnet gravity on fundamental metrics. This theory involves perturbative corrections to general relativity, as well as two scalar fields, the axion and the dilaton, that arise from Chern-Simons and Gauss-Bonnet gravity modifications respectively. The combined Chern-Simons-Gauss-Bonnet gravity is motivated by a wide range of theoretical and phenomenological perspectives, including particle physics, string theory, and parity violation in the gravitational sector. In this work, we provide the complete set of field equations and equations of motion of the Chern-Simons-Gauss-Bonnet modified gravity theory for a suite of fundamental metrics (Friedmann-Lemaitre-Robertson-Walker, Schwarzschild, spherically symmetric, and perturbed Minkowski), under no prior assumptions on the behavior of the fields. The full set of field equations and equations of motion can be numerically solved and applied to specific observables under certain assumptions, and can be used to place constraints on the Chern-Simons-Gauss-Bonnet modified gravity theory.