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The first comprehensive analyses of Planck data reveal that the cosmological model with dark energy and cold dark matter can satisfactorily explain the essential physical features of the expanding Universe. However, the inability to…
By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time)…
In this paper, we study the model of the late universe with the homogeneous, isotropic and flat Friedmann-Robertson-Walker metric, where the source of the gravitational field is based on the fermion and boson field, with the Maxwell term…
The observed matter in the universe accounts for just 5 percent of the observed gravity. A possible explanation is that Newton's and Einstein's theories of gravity fail where gravity is either weak or enhanced. The modified theory of…
In the class of metrics of a generic conformal structure there exists a distinguishing metric. This was noticed by Albert Einstein in a lesser-known paper of 1921 (Berl. Ber., 1921, pp. 261-264). We explore this finding from a geometrical…
On November 18, 1915 Einstein reported to the Prussian Academy that the perihelion motion of Mercury is explained by his new General Theory of Relativity: Einstein found approximate solutions to his November 11, 1915 field equations.…
There is general agreement that the universe began with an "explosion" of matter and energy at a "singularity", the "Big Bang". This paper analyses the mechanics of that beginning and two alternative theories related to it: - The…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a…
Vigneron [Foundations of Physics, 54, 15, (2024)] recently proposed a modification of general relativity in which a non-dynamical term related to the spatial topology is introduced in the Einstein equation. The original motivation for this…
There exists some confusion, as evidenced in the literature, regarding the nature of the gravitational field in Einstein's General Theory of Relativity. It is argued here the this confusion is a result of a change in interpretation of the…
Between 1905 and 1907, Einstein first tried to extend the special theory of relativity in such a way so as to explain gravitational phenomena. This was the most natural and simplest path to be taken. These investigations did not fit in with…
In this paper I describe the genesis of Einstein's early work on the problem of motion in general relativity (GR): the question of whether the motion of matter subject to gravity can be derived directly from the Einstein field equations. In…
In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of $n+1$-dimensional, $n \geq 3$, spatially compact spacetimes which generalizes the $k=-1$…
We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small…
The general idea to modify Einstein's field equations by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$ was apparently outlined for the first time in [12-15]. The modification itself originates from…
The Equivalence Principle (EP) is not one of the ``universal'' principles of physics (like the Action Principle). It is a heuristic hypothesis which was introduced by Einstein in 1907, and used by him to construct his theory of General…
In his Autobiographical Notes, Einstein mentioned that on his road to the final theory of general relativity it was a major difficulty to accustom himself to the idea that coordinates need not possess an immediate physical meaning in terms…
Extensions of Einstein gravity which allow the gravitational constant $G$ to change with time as the universe evolves may provide a resolution to the horizon problem without invoking a period of vacuum domination and without the subsequent…
We consider a non-singular origin for the Universe starting from an Einstein static Universe, the so called "emergent universe" scenario, in the framework of a theory which uses two volume elements $\sqrt{-{g}}d^{4}x$ and $\Phi d^{4}x$,…