Effective time variation of G in a model universe with variable space dimension

Time variation of the Newtonian gravitational constant, G, is studied in mo del universes with a variable space dimension proposed recently. Using the Lagrangian formulation of these models, we find the effective gravitational constant as a function of time. To compare it with observational data, a t est theory for the time variation of G is formulated. We have assumed a pow er law behavior of the time variation of G where the exponent beta is itsel f time dependent. Within this test theory we are able to restrict the free parameter of the theories under consideration and give upper bounds for the space dimension at the Planck era. The time variation of G at earlier time s, such as the time of nucleosynthesis is also predicted which express the needs to look for related observational data. (C) 1999 Published by Elsevie r Science B.V. All rights reserved.