Eur. Phys. J. C (2017) 77: 87
https://doi.org/10.1140/epjc/s10052-017-4653-8

Regular Article - Theoretical Physics

Chern–Simons gravity in four dimensions

¹ Departamento de Física, Universidade Federal de Viçosa (UFV), Viçosa, MG, Brazil
² Carrera de Física, Universidad Mayor de San Andrés, La Paz, Bolivia

^* e-mail: opiguet@pq.cnpq.br

Received: 16 January 2017
Accepted: 26 January 2017
Published online: 9 February 2017

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