Covariant extrinsic gravity and the geometric origin of dark energy

TL;DR

This paper develops a covariant framework for induced gravity on a brane in higher dimensions, linking dark energy to the extrinsic curvature of the brane, and aligns well with observations in an 11D bulk.

Contribution

It introduces a covariant, model-independent formalism connecting extrinsic geometry of the brane to dark energy, extending previous models with a new geometric perspective.

Findings

Dark energy density relates to brane width and extra dimensions.

Model predicts dark energy as extrinsic curvature effect.

Agreement with observations in 11-dimensional bulk.

Abstract

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. It is shown that the predictions of this model are in good agreement with observation if we consider an 11-dimensional bulk space.