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The nature of the gravitational interaction between ordinary and dark matter is still open. Any deviation from universality or the Newtonian law also modifies the standard assumption of collisionless dark matter. On the other hand,…
General relativity is exquisitely tested in strong-field regimes, yet its validity on cosmological scales remains largely unexplored. Upcoming wide and deep large-scale structure surveys will access the ultra-large, linear scales where…
The accuracy reached in the past few years by Satellite Laser Ranging (SLR) allows for measuring even tiny features of the Earth's gravitational field predicted by Einstein's General Relativity by means of artificial satellites. The…
We review attempts to estimate the influence of global cosmological expansion on local systems. Here `local' is taken to mean that the sizes of the considered systems are much smaller than cosmologically relevant scales. For example, such…
We study the consequences of the $f(R/\Box)$ gravity models for the Solar system and the large scale structure of the universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the…
The possibility of a Newtonian gravitomagnetic field is considered here with its immediate and far-reaching implications for the interpretation of 2004 LAGEOS experimental results confirming the general relativistic prediction of…
A novel experimental setup to measure deviations from the $1/r^2$ distance dependence of Newtonian gravity was proposed in arXiv:1609.05654. The underlying theoretical idea was to study the orbits of a microscopically-sized planetary system…
Since last two decades $f(R)$ gravity theory has been extensively used as a serious alternative of general relativity to mimic the effects of dark energy. The theory presents a Yukawa correction to Newtonian gravitational potential, acting…
Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, special relativity uses the assumption about the Euclidean structures of gravity-free…
Strong gravitational lensing provides a natural opportunity to test General Relativity (GR). We propose a model-independent method for simultaneous constraining on Hubble constant ($H_0$) and post-Newtonian parameter (${\gamma_{\rm{PPN}}}$)…
We explore, in the general relativistic context, the properties of the recently introduced GPS coordinates, as well as those of the associated frames and coframes. We show that they are covariant, and completely independent of any observer.…
In the pursuit of a general formulation for a modified gravitational theory at the non-relativistic level and as an alternative to the dark matter hypothesis, we construct a model valid over a wide variety of astrophysical scales. Through…
We study the cosmology of a covariant Galileon field with five covariant Lagrangians and confront this theory with the most recent cosmological probes: the type Ia supernovae data (Constitution and Union2 sets), cosmic microwave background…
In this paper we very preliminarily investigate the possibility of measuring the post-Newtonian general relativistic gravitoelectric and gravitomagnetic components of the acceleration of gravity on the Earth, in continuous regime, with two…
The generalized uncertainty principle and a minimum measurable length arise in various theories of gravity and predict Planck-scale modifications of the canonical position-momentum commutation relation. Postulating a similar modified…
General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived in the approximation of the linearized Einstein equations. All terms of order…
The four observables associated with gravitational lensing of distant quasars by intervening galaxies: image splittings, relative amplifications, time delays, and optical depths, provide separate measures of the strength of the…
The observed acceleration of the universe, explained through dark energy, could alternatively be explained through a modification of gravity that would also induce modifications in the evolution of cosmological perturbations. We use new…
This paper discusses three matter-of-principle methods for measuring the general relativity correction to the Newtonian values of the position of collinear Lagrangian points L1 and L2 of the Sun-Earth-satellite system. All approaches are…
The physical basis of the standard theory of general relativity is examined and a nonlocal theory of accelerated observers is described that involves a natural generalization of the hypothesis of locality. The nonlocal theory is confronted…