Chern–Simons gravity in four dimensions

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 ΛΛ CDM cosmological solutions of general relativity. We also check that vanishing torsion is a stable feature of the solutions.