# Chern-Simons Gravity in Four Dimensions

## TL;DR

This paper explores four-dimensional Chern-Simons gravity derived from five-dimensional theories, showing it reproduces key solutions of General Relativity and remains stable under certain conditions.

## Contribution

It demonstrates that 4D Chern-Simons gravity can replicate GR solutions like Schwarzschild-de Sitter and ΛCDM, with stable torsion-free solutions.

## Key findings

- Reproduces Schwarzschild-de Sitter solutions
- Matches ΛCDM cosmological solutions
- Shows stability of torsion-free configurations

## Abstract

Five dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to General Relativity with cosmological constant. We consider the zero-modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and $\Lambda$CDM cosmological solutions of General Relativity. We also check that vanishing torsion is a stable feature of the solutions.