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Cosmic transients, such as gamma-ray bursts and fast radio bursts, have been used to constrain the Einstein’s Equivalence Principle (EEP) through the parametrized-post-Newtonian (PPN) formalism. In this approach, the time delay of photons with different energies from these cosmic transients are used to obtain upper bounds on the difference of the PPN γ parameter. In this work we assume that an important contribution to the time delay is due to the dark matter halo of the Milky Way and consider the dark matter mass distribution given by the Navarro–Frenk–White profile. We obtain the upper limit on the difference of the PPN parameter γ for the polarized gamma-ray emission of GRB 110721A, Δ γ < 1 . 06 × 1 0 − 28 , the most stringent limit to date on the EEP. In addition, we show that a very similar upper bound is obtained if, instead of having a dark matter component, a visible matter density profile and a non-minimal gravitational coupling between curvature and matter are present. [ABSTRACT FROM AUTHOR]

We examine an extension of General Relativity with an explicit non-minimal coupling between matter and curvature. The purpose of this work is to present an overview of the implications of the latter to various contexts, ranging from astrophysical matter distributions to a cosmological setting. Various results are discussed, including the impact of this non-minimal coupling on the choice of Lagrangian density, on a mechanism to mimic galactic and cluster dark matter, on the possibility of accounting for the accelerated expansion of the Universe, energy density fluctuations and modifications to post-inflationary reheating. The equivalence between a model exhibiting a non-minimal coupling and multi-scalar-theories is also discussed. [ABSTRACT FROM AUTHOR]

We discuss the motivation for high accuracy relativistic gravitational experiments in the solar system and complementary cosmological tests. We focus our attention on the issue of distinguishing a generic scalar theory of gravity as the underlying physical theory from the usual general-relativistic picture, where one expects the presence of fundamental scalar fields associated, for instance, with inflation, dark matter and dark energy. [ABSTRACT FROM AUTHOR]