Four-dimensional Brane–Chern–Simons Gravity and Cosmology

Abstract

From the field equations corresponding to a four-dimensional brane embedded in the five-dimensional spacetime of the Einstein–Chern–Simons theory for gravity, we find cosmological solutions that describe an accelerated expansion for a flat universe. Apart from a quintessence-type evolution scheme, we obtain a transient phantom evolution, which is not ruled out by the current observational data. Additionally, a bouncing solution is shown. The introduction of a kinetic term in the action shows a de Sitter behavior although the energy density is not constant. A quintessence behavior is also found. We conjecture on a possible geometric origin of dark energy coming from this action.

Cosmology in 5D and 4D Einstein-Gauss-Bonnet gravity

“…The symbol ∼ denotes 4-dimensional quantities. We will use the usual notation [8], [9] x α = (x µ , φ) ; α, β = 0, ..., 4 ; a, b = 0, ..., 4; µ, ν = 0, ..., 3 ; m, n = 0, ..., 3 ;…”

“…From (3) we can see that the Lagrangian contains the Gauss-Bonnet term L GB , the Einstein-Hilbert term L EH and a cosmological term L Λ . In fact, replacing (55) and (60) in L GB , L EH , L Λ and using εmnpq = ε mnpq4 , we obtain [8], [9] L GB = ε abcde R ab R cd e e ,…”

“…dimensional vanishing torsion conditionT m = dẽ m + ωm n ẽn = 0, (59)where f ′ = ∂f /∂φ, ωm n = ω m n and d = dx µ ∂/∂ xµ . From (58), (59) and the Cartan's second structural equation, R ab = dω ab + ω a c ω cb , we obtain the components of the 2-form curvature[8],[9] …”

Cosmology in 5D and 4D Einstein–Gauss–Bonnet gravity

“…The symbol ∼ denotes 4-dimensional quantities. We will use the usual notation [20,21] x α = xμ , φ ; α, β = 0, . .…”

Five-dimensional Einstein-Chern-Simons cosmology

“…For instance, in the framework of braneworld cosmology, in Refs. [15,16] the h-field was associated with a scalar field, exhibiting the behavior of cosmological constant (dark energy). This background could then lead to a response to the concern presented.…”