2 research outputs found
Einstein equations for an asymmetric brane-world
We consider a brane-world of co-dimension one without the reflection symmetry
that is commonly imposed between the two sides of the brane. Using the
coordinate-free formalism of the Gauss-Codacci equations, we derive the
effective Einstein equations by relating the local curvature to the matter on
the brane in the case when its bare tension is much larger than the localized
matter, and hence show that Einstein gravity is a natural consequence of such
models in the weak field limit. We find agreement with the recently derived
cosmological case, which can be solved exactly, and point out that such models
can be realized naturally in the case where there is a minimally coupled form
field in the bulk.Comment: 14 pages, Revte
The Dynamics of Brane-World Cosmological Models
Brane-world cosmology is motivated by recent developments in string/M-theory
and offers a new perspective on the hierarchy problem. In the brane-world
scenario, our Universe is a four-dimensional subspace or {\em brane} embedded
in a higher-dimensional {\em bulk} spacetime. Ordinary matter fields are
confined to the brane while the gravitational field can also propagate in the
bulk, leading to modifications of Einstein's theory of general relativity at
high energies. In particular, the Randall-Sundrum-type models are
self-consistent and simple and allow for an investigation of the essential
non-linear gravitational dynamics. The governing field equations induced on the
brane differ from the general relativistic equations in that there are nonlocal
effects from the free gravitational field in the bulk, transmitted via the
projection of the bulk Weyl tensor, and the local quadratic energy-momentum
corrections, which are significant in the high-energy regime close to the
initial singularity. In this review we discuss the asymptotic dynamical
evolution of spatially homogeneous brane-world cosmological models containing
both a perfect fluid and a scalar field close to the initial singularity. Using
dynamical systems techniques it is found that, for models with a physically
relevant equation of state, an isotropic singularity is a past-attractor in all
orthogonal spatially homogeneous models (including Bianchi type IX models). In
addition, we describe the dynamics in a class of inhomogeneous brane-world
models, and show that these models also have an isotropic initial singularity.
These results provide support for the conjecture that typically the initial
cosmological singularity is isotropic in brane-world cosmology.Comment: Einstein Centennial Review Article: to appear in CJ