Brane Cosmology and Motion of Test Particles in Five-Dimensional Warped Product Spacetimes

TL;DR

This paper investigates the motion and confinement of test particles in a five-dimensional warped spacetime with a non-compact extra dimension, analyzing geodesics, stability, and cosmological implications within braneworld models.

Contribution

It introduces a model with exponential warping depending on time and extra coordinates, studying particle geodesics and stability in this novel geometrical setup.

Findings

Test particles can be confined under certain conditions.

Stability of geodesics depends on the warp and lapse functions.

Cosmological models of the 4D hypersurfaces are discussed.

Abstract

In the braneworld scenario ordinary standard model matter and on-gravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the bulk (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product space-time having an exponential warping function which depends both on time as well as on the extra coordinates and a non-compact fifth dimension. Further, we have assumed that the lapse function may either be a constant or a function of both time and of the extra coordinates, and have studied the nature of the geodesics of test particles and analyzed the conditions of stability in this geometrical framework. We have also discussed the possible cosmology of the corresponding (3 + 1)-dimensional hypersurfaces.