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We discuss the advantages of using metric theories of gravity with curvature-matter couplings in order to construct a relativistic generalisation of the simplest version of Modified Newtonian Dynamics (MOND), where Tully-Fisher scalings are valid for a wide variety of astrophysical objects. We show that these proposals are valid at the weakest perturbation order for trajectories of massive and massless particles (photons). These constructions can be divided into local and non-local metric theories of gravity with curvature-matter couplings. Using the simplest two local constructions in a FLRW universe for dust, we show that there is no need for the introduction of dark matter and dark energy components into the Friedmann equation in order to account for type Ia supernovae observations of an accelerated universe at the present epoch.
We explore the viability of a bulk viscous matter-dominated Universe to explain the present accelerated expansion of the Universe. The model is composed by a pressureless fluid with bulk viscosity of the form zeta = zeta_0 + zeta_1 * H where zeta_0 a
We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor structure into con
We investigate if a recently introduced formulation of general relativity on a Weyl-integrable geometry, contains cosmological solutions exhibiting acceleration in the present cosmic expansion. We derive the general conditions to have acceleration in
We propose a class of theories that can limit scalars constructed from the extrinsic curvature. Applied to cosmology, this framework allows us to control not only the Hubble parameter but also anisotropies without the problem of Ostrogradsky ghost, w
In this paper we will provide a non-singular rotating space time metric for a ghost free infinite derivative theory of gravity. We will provide the predictions for the Lense-Thirring effect for a slowly rotating system, and how it is compared with that from general relativity.