The Principle of Equivalence and Cosmological Metrics

This paper is concerned with the extent to which the geodesics of space-time (that is, the experimental consequences of the principle of equivalence) determine the metric in general relativity theory and, in particular, in Friedmann-Robertson-Walker-Lemaitre (FRWL) space-times. Thus it discusses projective structure in these space-times. The approach will be from a geometrical point of view and it is shown that if two space-time metrics share the same (unparametrized) geodesics and one is a (generic) FRWL metric then so is the other and that each is a member of a well defined family of projectively related (FRWL) metrics. Similar techniques are then applied to study the existence and properties of symmetries of the Weyl projective tensor and projective symmetries in FRWL space-times.