Variation of G, ${\Lambda }_{(4)}$ 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 $g_{4\mu }=0$ 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 $g_{44}=\epsilon {\Phi }^2$, where $\epsilon =\pm 1$ and $\Phi$ is a scalar function varying with time, $\dot{\Phi }\ne 0$. 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 {\em fixed} brane and use the brane-world paradigm to determine the fundamental parameters in the theory, which are the vacuum energy $\sigma$, the gravitational coupling $G$ and the cosmological term ${\Lambda }_{(4)}$. 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 $\dot{G}/G\sim H$ and ${\Lambda }_{(4)}\sim H^2$, 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 $\dot{\Phi }=0$. We conclude that the introduction of a time-varying $\Phi$ in brane-world theory yields a number of models that show variation in the fundamental physical "constants" and exhibit reasonable physical properties.

In version 2 an error noticed by the author is fixed, and the corresponding changes are made. Version 3 is identical to v2, except for a couple of typos corrected. V3 will appear in Mod. Phys. Lett. A

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