Covariant extrinsic gravity and the geometric origin of dark energy

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.Comment: 29 pages, 2 figures, revised versio

Why the measured cosmological constant is small

“…Hence, one may be able to argue that cosmological constant, or dark energy, has really a gravitational-geometrical origin and is not connected to the vacuum energy. To solve the cosmological constant problem, following [1], we introduced a new gravitational model in which our spacetime is embedded in the ambient space with seven extra dimensions. The use of Nash-Morse implicit function theorem, lets the embedded spacetime to have a thickness.…”

“…Nash's strategy, which is also the strategy of later authors, was to consider the problem of perturbing a given isometric embedding to achieve some desired and suitably small change in the metric [14,15,16]. Suppose the local coordinates 1 Greek indices run from 0 to 3, small case Latin indices run from 4 to D − 1 and large Latin indices run from 0 to D − 1. Units so that = c = 1 are used throughout this work.…”

“…where G 0 and g 0i are the gravitational constant and gauge coupling constants at the present epoch, respectively. Then, the induced Einstein-Yang-Mills field equations for the thick brane world model will be [1]…”

“…Then additional assumptions are needed to specify the extrinsic curvature. It was shown that, the induced gravitational constant, G N , depended on the local normal radii of the Freidmann-Lamaître-Robertson-Walker (FLRW) submanifold, an arbitrary function of the cosmic time [1]. In this paper, to be able to solve the resulting field equations, we will use a simple phenomenological power law form of G N in terms of scale factor.…”

Emergent universe in the braneworld scenario

“…Note that we have not included the cosmological constant because it is possible to construct a geometrical origin for the dark energy in a general geometrical embedding scheme with a brane possessing an extrinsic curvature, to recover the acceleration of the Universe [103,122]. The generalization to the case that the cosmological constant is not zero is trivial.…”