Accelerated FRW Solutions in Chern-Simons Gravity

Abstract

We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter, where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion and hyperbolic expansion when $\alpha$, a parameter of theory, is greater than zero. This result allow us to conjeture that this solutions are compatible with the era of Dark Energy and that the energy-momentum tensor for the field $h^a$, a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion ($\alpha >0$) with a minimum scale factor at initial time that, when the time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describing an accelerated expansion whose scale factor behaves as a exponencial function when time grows. \item In the case of a closed universe it is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function when time grows.

58 pages, 24 figures

References in corpus (9)

• Expanding Lie (super)algebras through abelian semigroups
• Topological gravity and transgression holography
• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• General Relativity from a gauged WZW term
• Solutions of Higher Dimensional Gauss-Bonnet FRW Cosmology
• The Universe as a topological defect
• Black hole for the Einstein-Chern-Simons gravity
• Topological gravity and Wess-Zumino-Witten term
• Some considerations on the Mac Dowell-Mansouri action

Cited by in corpus (9)

• Generalized Galilean Algebras and Newtonian Gravity
• Five-dimensional Einstein-Chern-Simons cosmology
• Four-dimensional Brane-Chern-Simons Gravity and Cosmology
• Brane gravity in 4D from Chern-Simons gravity theory
• Static solutions in Einstein-Chern-Simons gravity
• On a Java library to perform S-expansions of Lie algebras
• A Java library to perform S-expansions of Lie algebras
• Einstein-Chern-Simons equations on the 3-brane world
• Cosmology from Newton-Chern-Simons gravity