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.

The large-number hypothesis conjectures that fundamental constants may vary. Accordingly, the spacetime variation of fundamental constants has been an active subject of research for decades. Recently, using data obtained with large telescopes a phenomenological model in which the fine structure constant might vary spatially has been proposed. We test whether this hypothetical spatial variation of α, which follows a dipole law, is compatible with the data of distant thermonuclear supernovae. Unlike previous works, in our calculations we consider not only the variation of the luminosity distance when a varying α is adopted, but we also take into account the variation of the peak luminosity of Type Ia supernovae resulting from a variation of α. This is done using an empirical relation for the peak bolometric magnitude of thermonuclear supernovae that correctly reproduces the results of detailed numerical simulations. We find that there is no significant difference between the several phenomenological models studied here and the standard one, in which α does not vary spatially. We conclude that the present set of data of Type Ia supernovae is not able to distinguish the standard model from the dipole models, and thus cannot be used to discard nor to confirm the proposed spatial variation of α.

We analyse the MOdified Gravity (MOG) theory, proposed by Moffat, in a cosmological context. We use data from Type Ia Supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO) and Cosmic Chronometers (CC) to test MOG predictions. For this, we perform χ 2 tests considering fixed values of H0 and VG, the self-interaction potential of one of the scalar fields in the theory. Our results show that the MOG theory is in agreement with all data sets for some particular values of H0 and VG, being the BAO data set the most powerful tool to test MOG predictions, due to its constraining power.

Using a novel and self-consistent approach that avoids the scalar-tensor identification in the Einstein frame, we reanalyze the viability of f (R) gravity within the context of solar-system tests. In order to do so, we depart from a simple but fully relativistic system of differential equations that describe a compact object in a static and spherically symmetric spacetime, and then make suitable linearizations that apply to non-relativistic objects such as the Sun. We then show clearly under which conditions the emerging chameleon-like mechanism can lead to a Post-Newtonian Parameter γ compatible with the observational bounds. To illustrate this method, we use several specific f (R) models proposed to explain the current acceleration of the Universe, and we show which of them are able to satisfy those bounds. PACS numbers: 04.50.Kd, 95.36.+x, 04.40.Dg I. INTRODUCTIONf (R) gravity remains one of the most popular and viable mechanisms to explain the current accelerated expansion of the Universe (see Refs [1-6] for a review) while predicting an equation of state for the "dark energy" that changes in cosmic time and that might accommodate to future observations better than a simple cosmological constant Λ [7-9]. This proposal consists of taking for the action functional a (non linear) function f (R) of the Ricci scalar R different from the General Relativity (GR) f GR (R) = R − 2Λ. Thus, unless otherwise stated, and in order to avoid confusion, hereafter f (R) refers to those non-linear models. This alternative, while very attractive for it does not require additional fields, opens, however, a Pandora box that risks spoiling many of the GR predictions that have been verified with high accuracy during the past hundred years (e.g. solar-system tests, binary pulsar phenomenology), including the recent detection of gravitational waves by the LIGO-VIRGO collaboration [10]. Several specific f (R) models have been put forward to explain the cosmic acceleration, but many of them have failed other tests, including more refined cosmological scrutinies (e.g. the analysis of cosmological perturbations and the CMB), solar system (weak gravity tests) and strong gravity tests (e.g. neutron stars). One of the drawbacks of this kind of modifications of gravity is that there is a priori no fundamental principle