Related papers: Constraining Mach's principle with high precision …
A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In…
The Cosmological Principle is the assumption that the universe is spatially homogeneous and isotropic in the large-scale average. In year 1998 the author, together with his two colleagues, has shown that the BATSE's short gamma-ray bursts…
Recently, several interesting proposals were made modifying the law of gravity on large scales, within a sensible relativistic formulation. This allows a precise formulation of the idea that such a modification might account for galaxy…
We phenomenologically put local constraints on the rotation of distant masses by using the planets of the solar system. First, we analytically compute the orbital secular precessions induced on the motion of a test particle about a massive…
Well-known to specialists but little-known to the wider audience is that Newtonian gravity can be understood as geodesic motion in space-time, where time is absolute and space is Euclidean. Newtonian cosmology formulated by Heckmann agrees…
This paper is devoted to a practical model for relativistic reduction of positional observations with an accuracy of 1 \muas which is expected to be attained in the future space astrometry missions. All relativistic effects which are caused…
The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because…
The general theory of relativity (GR) has excelled in explaining gravitational phenomena at the scale of the solar system with remarkable precision. However, when extended to the galactic or cosmological scale, it requires dark matter and…
In meteorology the analysis of motions of the atmosphere on the Earth has been done using various mathematical models and using various approximations. In this article as the simplest model the compressible Euler equations with barotropic…
The search for the physical mechanism underlying the observational evidence for the acceleration of the recent universe is a compelling goal of modern fundamental cosmology. Here we quantitatively study a class of homogeneous and isotropic…
A generic second-order scalar-tensor theory contains a nonlinear derivative self-interaction of the scalar degree of freedom $\phi$ \`{a} la Galileon models, which allows for the Vainshtein screening mechanism. We investigate this effect on…
A mechanism is introduced to reduce a large cosmological constant to a sufficiently small value consistent with observational upper limit. The basic ingradient in this mechanism is a distinction which has been made between the two unit…
$f(R)$ theories of modified gravity may be compatible with current observations if the deviations from general relativity are sufficiently well screened in dense environments. In recent work [arXiv:2310.19955] we have shown that…
The Cosmological Principle states that the universe is both homogeneous and isotropic. This, alone, is not enough to specify the global geometry of the spacetime. If we were able to measure both the Hubble constant and the energy density we…
Future weak lensing surveys will map the evolution of matter perturbations and gravitational potentials, yielding a new test of general relativity on cosmic scales. They will probe the relations between matter overdensities, local…
Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of…
Using the Fisher matrix formalism, we quantitatively investigate the constraints on a 10 dimensional space of cosmological parameters which may be obtained with future cluster surveys. We explore the dependence of the Omega_m constraint on…
We consider the no-boundary proposal for homogeneous isotropic closed universes with a cosmological constant and a scalar field with a quadratic potential. In the semi-classical limit, it predicts classical behavior at late times if the…
Ghost-free bimetric gravity is a theory of two interacting spin-2 fields, one massless and one massive, in addition to the standard matter particles and fields, thereby generalizing Einstein's theory of general relativity. To parameterize…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…