ar X iv : g r - qc / 0 20 70 01 v 3 2 7 N ov 2 00 2 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 an external condition, not a requirement of the field equations. In this paper we study the consequences of having g 44 = ǫΦ 2 , where ǫ = ±1 and Φ is a scalar function varying with time, ˙ Φ = 0. This varying field entails the possibility of variable fundamental physical " constants ". These variations are different from those predicted in scalar-tensor and multidimensional theories. We solve the five-dimensional equations for a fixed brane and use the brane-world paradigm to determine the fundamental parameters in the theory, which are the vacuum energy σ, the gravitational coupling G and the cosmological term Λ (4). We present specific models where these physical quantities are variable functions of time. Different scenarios are possible but we discuss with some detail a model for which ˙ G/G ∼ H and Λ (4) ∼ H 2 , which seems to be favored by observations. Our results are not in contradiction to previous ones in the literature. In particular, to those where the brane is described as a domain wall moving in a static Sch − AdS bulk. Indeed these latter models in RS scenarios describe the same spacetime as other solutions (with fixed brane) in gaussian coordinates with ˙ Φ = 0. We conclude that the introduction of a time-varying Φ in brane-world theory yields a number of models that show variation in the fundamental physical " constants " and exhibit reasonable physical properties.