ar X iv : g r - qc / 0 20 70 01 v 1 2 9 Ju n 20 02 Variation of G , Λ ( 4 ) and Vacuum Energy From Brane - World Models

In brane-world theory in five dimensions, the bulk metric is usually written in gaussian coordinates, where g 4µ = 0 and g 44 = −1. However, the choice g 44 = −1 is not mandatory. The presence of matter in the brane can generate temporal and spatial variations of g 44 , which in turn backreact on the brane. In this paper we study the consequences of having g 44 = ǫΦ 2 , where ǫ = ±1 and Φ is a scalar function, not a constant. This extra field induces new features in the four-dimensional picture. Firstly, we find that the variable scalar field Φ demands the variation of at least two of the fundamental parameters in the theory, which are the vacuum energy λ, the gravitational coupling G and the cosmological term Λ (4). These variations are different from those predicted in scalar-tensor and multidimensional theories. Secondly, the conserved energy-momentum tensor on the brane represents a mixture of two fluids, a perfect fluid, with effective energy density Φρ and effective pressure Φp, and a vacuum fluid ρ v = −p v = −Φλ. This interpretation is independent of any particular assumption regarding the variation of λ, G and/or Λ (4). Also, we show that the construction of realistic astrophysical and cosmological models, of perfect fluid with inhomogeneous energy density, does not necessarily require a departure from an exact AdS 5 bulk. This departure can be avoided if we demand Φ to be spatially inhomogeneous. Finally we present a simple model that illustrates different physical scenarios for the variation of λ, G and Λ (4) within the context of brane-world theory.