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In general, modified gravity theories are modifications or extensions of Einstein's general relativity. Some of them give rise to additional scalar degrees of freedom in Nature. If these scalar fields exist and are light enough, they should…
We consider alternative theories of gravity with a direct coupling between matter and the Ricci scalar We study the relation between these theories and ordinary scalar-tensor gravity, or scalar-tensor theories which include non-standard…
MOdified Gravity (MOG) is a covariant modification of Einstein's general relativity. This theory is one of the current alternatives to dark matter models. We describe dynamics of collisionless self-gravitating systems in the context of MOG.…
The shadows cast by non-rotating and rotating modified gravity (MOG) black holes are determined by the two parameters mass $M$ and angular momentum $J=Ma$. The sizes of the shadows cast by the spherically symmetric static Schwarzschild-MOG…
We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the presence of dark matter, is the result of the dynamical evolution of particles in higher dimensional…
In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions…
It is a well known fact that, in the absence of Dark Matter, the observation of the rotation curves of galaxies cannot be explained in terms of Newtonian gravity. Rotation curves become flat in the outer regions, in contrast to what is…
It is shown that so-called dark energy could possible be a manifestation of the gravitational vortex producing the "gravitomagnetic" (GM) force field: associated with cosmic matter rotation and inertial spacetime frame dragging. The general…
The confrontation between Einstein's gravitation theory and experimental results, notably binary pulsar data, is summarized and its significance discussed. Experiment and theory agree at the 10^{-3} level. All the basic structures of…
An interaction between dark matter and dark energy is usually introduced by a phenomenological modification of the matter conservation equations, while the Einstein equations are left unchanged. Starting from some general and fundamental…
We investigate the possibility of dark matter being a pure geometrical effect, rather than a particle or a compact object, by exploring a specific modified gravity model: mimetic dark matter. We present an alternative formulation of the…
The evidence for the observation of the Higgs spin-0-boson as a manifestation of a scalar field provides the missing corner stone for the standard model of particles (SM). However, the SM fails to explain the non-visible but gravitationally…
We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved and there is…
The Einstein Telescope and other third generation interferometric detectors of gravitational waves are projected to be operational post $2030$. The cosmological signatures of gravitational waves would undoubtedly shed light on any departure…
Although general relativity (GR) passes all present experimental tests with flying colors, it remains important to study alternative theories of gravity for several theoretical and phenomenological reasons that we recall in these lecture…
Alternative theories of gravity predict the presence of massive scalar, vector, and tensor gravitational wave modes in addition to the standard massless spin~2 graviton of general relativity. The deflection and frequency shift effects on…
It is a well-known truism, inspired on the general theory of relativity, that gravity gravitates. Here we suggest the possibility that dark matter may be caused by the gravitation of the metric. At first sight this seems impossible since…
Cosmological scalar perturbation theory studied in the Newtonian gauge depends on two potentials $\Phi$ and $\Psi$. In General Relativity (GR) they must coincide ($\Phi=\Psi$) in the absence of anisotropic stresses sourced by the energy…
A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify…
In this contribution to the conference "Beyond Einstein: Historical Perspectives on Geometry, Gravitation and Cosmology in the Twentieth Century", we give a critical status report of attempts to explain the late accelerated expansion of the…