@MISC{Drummond_variablelight-cone, author = {I. T. Drummond}, title = {Variable Light-Cone Theory of Gravity}, year = {} }

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Abstract

We show how to reformulate Variable Speed of Light Theories (VSLT) in a covariant fashion as Variable Light-Cone Theories (VLCT) by introducing two vierbein bundles each associated with a distinct metric. The basic gravitational action relates to one bundle while matter propagates relative to the other in a conventional way. The variability of the speed of light is represented by the variability of the matter light-cone relative to the gravitational light-cone. The two bundles are related locally by an element M, of SL(4,R). The dynamics of the field M is that of a SL(4,R)-sigma model gauged with respect to local (orthochronous) Lorentz transformations on each of the bundles. Only the “massless ” version of the model with a single new coupling, F, that has the same dimensions as Newton’s constant GN, is considered in this paper. When F vanishes the theory reduces to standard General Relativity. We verify that the modified Bianchi identities of the model are consistent with the standard conservation law for the matter energy-momentum tensor in its own background metric. The implications of the model for some simple applications are examined. We discuss the Newtonian limit, the appropriate generalisations of the flat FRW universe and the spherically symmetric static solution. We conclude that the variability of the speed of light in the early universe is a possible homogenising mechanism. However an examination of the post-Newtonian approximation shows that on the basis of the results of VLBI measurements, the new coupling satisfies F/GN < 3.2 × 10 −4. We point out that other “massive ” versions of the model with different asymptotic properties may still permit consistency with General Relativity at large distances while predicting departures at short distances. DAMTP-99-102 1 1