Geometric scalar theory of gravity

Abstract

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. Some consequences of the new scalar theory are explored.

More about scalar gravity

“…In this paper (and in the two preceding ones [16,17]) we take a huge jump backwards by reconsidering models based just on a single scalar field. As a possible way out of some of the difficulties that Nordström's theories have because of the conformal prior (1) we explore the possibility that the physical metric be related to the Minkowski metric by a disformal transformation.…”

“…However, to the best of our knowledge, the model presented in [16] is the first (and up to now the only) one where a scalar field disformally coupled is used to modify the original Nordström's idea and describe gravity in the context of purely scalar theory.…”

“…Some features of this model were already explored in [16] and [17]. It is more or less obvious from the very beginning that the model cannot fit into the standard Parametrized Post-Newtonian (PPN) formalism as described in [10].…”

“…The class of models introduced in this way includes in particular a model that we have studied in two preceding papers (GSG) One of the criteria used to select this model [16] was the requirement that it should admit the Schwarzschild solution. We have deepened the discussion about this point and see that the disformal hypothesis is more subtle than one may think at first sight.…”

“…Following Feyerabend's counterrule, in two recent papers [16,17] we went back to that old failed idea and tried to improve it by introducing and beginning to explore a toy model of gravity based on a single scalar field which in a way overcomes certain difficulties of the old times. Here we continue that investigation to see how far we can go.…”