Applications of braneworld models to the theory of gravitation

Abstract

I have presented an evolving wormhole solution in braneworld model. Moreover I have shown that there are observational signatures for using braneworld to solve dark matter problem.

Braneworld assumed that four dimensional spacetime embedded into five dimensional bulk. Gravity is a five dimensional interaction and the usual four dimensional description is reproduced by geometric projection. It predicts correction terms to the Einstein equation, for instance, the higher dimensional Weyl curvature projected on the brane.

This projected Weyl curvature could make braneworld wormhole satisfies the Null Energy Condition (NEC), which is impossible in general relativity. We considered inflating braneworld wormhole that enlarge with the Universe, the wormhole is supported by the Weyl curvature so that it satisfies NEC. We demonstrated how this wormhole embedded into a five dimensional bulk and studied how it evolve with our Universe. The result is that inflating wormhole satisfying general initial condition will collapse into black hole when the scalar field oscillates.

In addition, the projected Weyl curvature introduces a new source of gravity. This Weyl fluid of geometrical origin (reducing in the spherically symmetric, static configuration to a dark radiation and dark pressure) modifies space-time geometry around galaxies and has been used to explain the flatness of galactic rotation curves. Independent observations for discerning between the Weyl fluid and other dark matter models are necessary. Gravitational lensing could provide such a test. Therefore we study null geodesics and weak gravitational lensing in

the dark radiation dominated region of galaxies in a class of spherically symmetric braneworld metrics. We find that the lensing profile in the braneworld scenario is distinguishable from dark matter lensing, despite both the braneworld scenario and dark matter models can fit the rotation curve data. In particular, in the asymptotic regions light deflection is 18% enhanced as compared to dark matter halo predictions. For a linear equation of state of the Weyl fluid we further find a critical radius, below which braneworld effects reduce, while above it they amplify light deflection. This is in contrast to any dark matter model, which

always increases the deflection angle.