VARIATION OF G, Λ(4) AND VACUUM ENERGY FROM BRANE-WORLD MODELS

Abstract

In brane-world theory in five dimensions, the bulk metric is usually written in Gaussian coordinates, where g4μ = 0 and g44 = -1. However, the choice g44 = -1 is an external condition, not a requirement of the field equations. In this paper we study the consequences of having g44 = εΦ2, where ε = ±1 and Φ is a scalar function varying with time, [Formula: see text]. 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 Ġ/G ~ H and Λ(4) ~ H2, 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 space–time as other solutions (with fixed brane) in Gaussian coordinates with [Formula: see text]. 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.