5 research outputs found
Chern-Simons theory and three-dimensional surfaces
There are two natural Chern-Simons theories associated with the embedding of
a three-dimensional surface in Euclidean space; one is constructed using the
induced metric connection -- it involves only the intrinsic geometry, the other
is extrinsic and uses the connection associated with the gauging of normal
rotations. As such, the two theories appear to describe very different aspects
of the surface geometry. Remarkably, at a classical level, they are equivalent.
In particular, it will be shown that their stress tensors differ only by a null
contribution. Their Euler-Lagrange equations provide identical constraints on
the normal curvature. A new identity for the Cotton tensor is associated with
the triviality of the Chern-Simons theory for embedded hypersurfaces implied by
this equivalence. The corresponding null surface stress capturing this
information will be constructed explicitly.Comment: 10 pages, unnecessary details removed, typos fixed, references adde
Modified geodetic brane cosmology
We explore the cosmological implications provided by the geodetic brane
gravity action corrected by an extrinsic curvature brane term, describing a
codimension-1 brane embedded in a 5D fixed Minkowski spacetime. In the geodetic
brane gravity action, we accommodate the correction term through a linear term
in the extrinsic curvature swept out by the brane. We study the resulting
geodetic-type equation of motion. Within a Friedmann-Robertson-Walker metric,
we obtain a generalized Friedmann equation describing the associated
cosmological evolution. We observe that, when the radiation-like energy
contribution from the extra dimension is vanishing, this effective model leads
to a self-(non-self)-accelerated expansion of the brane-like universe in
dependence on the nature of the concomitant \beta-parameter associated with the
correction, which resembles an analogous behaviour in the DGP brane cosmology.
Several possibilities in the description for the cosmic evolution of this model
are embodied and characterized by the involved density parameters related in
turn to the cosmological constant, the geometry characterizing the model, the
introduced \beta-parameter as well as the dark like-energy and the matter
content on the brane.Comment: 15 pages, 3 figures. New version corresponds to the one published in
CQ