Dimensionally compactified Chern-Simon theory in 5D as a gravitation theory in 4D

TL;DR

This paper derives a 4D gravitational theory from a 5D topological Chern-Simons theory via compactification, resulting in a model that includes torsion and reproduces key cosmological solutions.

Contribution

It introduces a novel approach to gravity by compactifying 5D Chern-Simons theory with de Sitter or anti-de Sitter groups, leading to a 4D theory with torsion.

Findings

Reproduces Lambda-CDM cosmology with zero torsion

Obtains a realistic spherically symmetric solution

Shows torsion can be non-zero in the theory

Abstract

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) -- the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.