Inhomogeneous Gravity

W e study the inhom ogeneous cosm ologicalevolution ofthe Newtonian gravitational ’constant’ G in the fram ework ofscalar-tensortheories.W e investigatethe di(cid:11)erences thatarise between the evolution of G in the background universesand in localinho-m ogeneitiesthathaveseparated outfrom theglobalexpansion.Exactinhom ogeneous solutions are found which describe the e(cid:11)ects ofm asses em bedded in an expanding FRW Brans-D icke universe.These are used to discuss possible spatialvariations of G in di(cid:11)erent regions.W e develop the technique ofm atching di(cid:11)erent scalar-tensor cosm ologies ofdi(cid:11)erent spatialcurvature at a boundary.This provides a m odelfor the linear and non-linear evolution ofsphericaloverdensities and inhom ogeneities in G : Thisallowsusto com paretheevolution of G and _ G thatoccursinsidea collapsing overdenseclusterwith thatin thebackground universe.W