results of the detailed analyses indicate that those world-lines do not, in general, correspond to geodesics. Quantum aspects further complicate the analysis of the motion of even the simplest things, which one might want to take as paradigmatic point like objects, such as photons [4]. Even though such UFF violating effects are normally very small, they are always there in principle, and therefore these considerations should serve as warnings when we go on to analyze more complex situations.Of particular interest for us here will be any theory in which the local coupling constants are taken to be effectively space-time dependent, while respecting the principles of locality and general covariance, as those entail some kind of fundamental field controlling the spatial dependence, with the field, generically, coupling in different manners to the various types of matter. Such field, usually taken to be a scalar field, generically mediates new forces between macroscopic objects, which would look, at the empirical level, as modifications of gravitation which might, in principle, lead to effective violations of the UFF for test bodies in external gravitational fields. For this reason, most theories that predict variations of fundamental constants also predict effective violations of the WEP [5][6][7][8][9]. For instance, the rest energy of a macroscopic body is made of many contributions related to the energies associated with various kinds of interactions (strong, weak, electromagnetic) and such components would be affected differently by a light scalar field. From the experimental point of view, one needs to confront the very strong limits on possible violations of the WEP that come from Eötvös-Roll-Krotkov-Dicke and Braginsky-Panov experiments and their modern reincarnations [10-15] which explore the differential acceleration of test bodies in gravitational contexts. In fact current bounds reach sensitivities of order ∆a a ≃ 10 −13 (or more), and thus can, in principle, constrain the viability of many models. Recently, there has been a great level of interest in models that claim to be able to avoid the stringent bounds resulting from experimental tests looking for violations of the WEP based on schemes where the effects of the fields are hidden by suitable non-linearities, as in the chameleon models and the Dilaton-Matter-gravity model with strong coupling [16]. Chameleon models were introduced by Khoury and Weltman in 2004 [1] and have been further developed by several authors [18][19][20][21][22][23][24][25]27]. Generically a chameleon consists of a scalar field that is coupled non-minimally to matter and minimally to the curvature (or the other way around via a conformal transformation), and where the field's effective mass depends on the density and pressure of the matter that constitutes the environment. This, in turn, is the result of the nontrivial coupling of the scalar field with the trace of the energy-momentum tensor of the matter sector of the theory 1 . The coupling of the scalar field with matter might...

"The self-induced collapse hypothesis" was introduced by D. Sudarsky and collaborators to explain the origin of cosmic structure from a perfect isotropic and homogeneous universe during the inflationary regime. In this paper, we calculate the power spectrum for the tensor modes, within the semiclassical gravity approximation, with the additional hypothesis of a generic self-induced collapse of the inflaton's wave function; we also compute an estimate for the tensor-to-scalar ratio. Based on this calculation, we show that the considered proposal exhibits a strong suppression of the tensor modes amplitude; nevertheless, the corresponding amplitude is still consistent with the joint BICEP/KECK and Planck Collaboration's limit on the tensor-to-scalar ratio.Comment: 18 pages, 2 figures. Replaced to match published versio

Bekenstein has shown that violation of Weak Equivalence Principle is strongly supressed in his model of charge variation. In this paper, it is shown that nuclear magnetic energy is large enough to produce observable effects in Eötvös experiments.

We perform a test of John Moffat's Modified Gravity theory (MOG) within the Milky Way, adopting the well known "Rotation Curve" method. We use the dynamics of observed tracers within the disk to determine the gravitational potential as a function of galactocentric distance, and compare that with the potential that is expected to be generated by the visible component only (stars and gas) under different "flavors" of the MOG theory, making use of a state-of-the-art setup for both the observed tracers and baryonic morphology. Our analysis shows that in both the original and the modified version (considering a self-consistent evaluation of the Milky Way mass), the theory fails to reproduce the observed rotation curve. We conclude that in none of its present formulation, the MOG theory is able to explain the observed Rotation Curve of the Milky Way.