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.

We describe what cosmology looks like in the context of the geometric theory of gravity based on a single scalar field. There are two distinct classes of cosmological solutions. An interesting feature is the possibility of having a bounce without invoking exotic equations of state for the cosmic fluid. We also discuss cosmological perturbation and present the basis of structure formation by gravitational instability in the framework of the geometric scalar gravity

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We perform a post-Newtonian (PN) solar system analysis for Palatini f (R) theories considering finite volume non-spherical planets and with emphasis to f (R) functions that are analytical about R = 0. First we consider the Will-Nordtvedt parametrized post-Newtonian (PPN) formalism, from which the metric is shown to depend, in general, on terms not covered by the standard PPN potentials. Hence, a full analysis of the PN equations of motion is performed. From the latter we conclude that, apart from redefinitions on the internal energy and the pressure, which cannot be constrained by solar system tests, the center-of-mass orbits are the same as in general relativity. We discuss further the physics of these redefinitions and use an argument to extend our analytical f (R) results towards some non-analytical functions. CONTENTS

We discuss a class of models for gravity based on a scalar field. The models include and generalize the old approach by Nordström which predated and in some way inspired General Relativity. The class include also a model that we have recently introduced and discussed in its cosmological aspects (GSG). We present here a complete characterisation of the Schwarschild geometry as a vacuum solution of GSG and sketch a discussion of the first Post-Newtonian approximation.