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 an accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion, and hyperbolic expansion when \(\alpha \), a parameter of the theory, is greater than zero. This result allows us to conjecture that these 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 time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describe an accelerated expansion whose scale factor behaves as an exponential function of time. (iii) In the case of a closed universe there is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function of time.