Covariant extrinsic gravity and the geometric origin of dark energy

Understand

We construct the covariant or model independent induced Einstein-Yang-Mills field equations on a 4-dimensional brane embedded isometrically in an D-dimensional bulk space, assuming the matter fields are confined to the brane.

• Applying this formalism to cosmology, we derive the generalized Friedmann equations.
• We derive the density parameter of dark energy in terms of width of the brane, normal curvature radii and the number of extra large dimensions.
• We show that dark energy could actually be the manifestation of the local extrinsic shape of the brane.