We present a geometric scalar theory of gravity. Our proposal will be described using the “background field method” introduced by Gupta, Feynman, Deser and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor—which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models—does not apply to our geometric scalar theory. From the very beginning this is not a special relativistic scalar gravity. The adjective “geometric” pinpoints its similarity with general relativity: this is a metric theory of gravity. Some consequences of this new scalar theory are explored.
Authors: M. Novello1, E. Bittencourt, U. Moschella, E. Goulart, J. M. Salim, and J. D. Toniato