Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model *

Abstract

We investigate a 6d generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. It is shown that each stress-energy tensor T i ab on the brane is similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model in which each 3-brane Lagrangian separated out a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5d Friedmann-Robertson-Walker field equations. At a little later period, the expansion of the universe is proportional to t 1 2 which is as similar as the period of the radiation-dominated. We also investigate the case with two a(t) and two b(t). In a large region of t, we obtain the 3d effective cosmological constant Λ ef f = −2Ω/3 > 0 which is independent of the integral constant. Here the scale factor is exponential expansion which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model which solves the dark energy problem, meanwhile guaranteeing a positive brane tension.

Cosmic Acceleration Caused by the Extra-Dimensional Evolution in a Generalized Randall-Sundrum Model

“…Variation with respect to the metric G AB and after some easy manipulations, then modulo surface terms, one obtains 7) where R AB is the (n + 1)-d Ricci tensor, T i AB is the (n + 1)-d energy-momentum tensors. Note here the energymomentum tensor is given by 45,46], A solution to the Eq. ( 7) with the metric tensor Eq.…”

“…where Ω is the induced cosmological constant on the visible brane, R and R ab are the n-d Ricci scalar and Ricci tensor respectively, Note that the solution derived above has the negative induced cosmological constant Ω, Here we do not consider the situation for Ω > 0, since the tension on the visible brane is negative which results in instability [29,39,45,46]. Then, an anisotropic metric is assumed to be of the following form [45][46][47]: 12) where a i is the scale factor. The case that the scale factors on the visible brane evolve with two different rates has been studied recently [46].…”

“…In this scenario, the tension of the visible brane and the hidden brane can be both positive with a negative induced cosmological constant. It is very interesting because that both branes are stable [40][41][42][43][44][45]. In order to be consistent with the current constraints, the negative induced cosmological constant Ω should be transformed into the positive effective cosmological constant Ω ef f .…”