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The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame (RF) to an uniformly accelerated RF…
Evaluation of the additive constants in the space-time Lorentz transformation equations required, according to Einstein, to correctly describe synchronised clocks at different spatial locations, reveals the spurious and unphysical nature of…
The behavior of one-dimensional Hegselmann-Krause (HK) dynamics driven by noise has been extensively studied. Previous research has indicated that within no matter the bounded or the unbounded space of one dimension, the HK dynamics attain…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on…
We describe how a certain simple modification of general relativity, in which the local cosmological constant is allowed to depend on the space-time curvature, predicts the existence of halos of modified gravity surrounding…
The laws of physics have a set of fundamental constants, and it is generally admitted that only dimensionless combinations of constants have physical significance. These combinations include the electromagnetic and gravitational fine…
We propose that the effective dimensionality of the space we live in depends on the length scale we are probing. As the length scale increases, new dimensions open up. At short scales the space is lower dimensional; at the intermediate…
Review of recent works devoted to the temporal and spatial variation of the fundamental constants and dependence of the fundamental constants on the gravitational potential (violation of local position invariance) is presented. We discuss…
We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of…
In cosmologies with more than four dimensions, of the type required for unification, it is possible for signals to have velocities in excess of that of light. Using a five-dimensional model which otherwise agrees with observations, two…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the…
Time delays in strong gravitational lensing systems possess significant complementarity with distance measurements to determine the dark energy equation of state, as well as the matter density and Hubble constant. Time delays are most…
The emergence of a highly improbable coincidence in cosmological observations speaks to a remarkably simple cosmic expansion. Compelling evidence now suggests that the Universe's gravitational horizon, coincident with the better known…
Observational manifestations of some models of modified gravity, which have been suggested to explain the accelerated cosmological expansion, are analyzed for gravitating systems with time dependent mass density. It is shown that if the…
The higher dimensional cosmology provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Here we discuss two situations where starting with an ordinary matter field without any equation of state…
We formulate the transition from decelerated to accelerated expansion as a bounce in connection space and study its quantum cosmology, knowing that reflections are notorious for bringing quantum effects to the fore. We use a formalism for…
In this paper we discuss a possible cosmological time evolution of fundamental constants from the theoretical and experimental point of views. On the theoretical side, we explain that such a cosmological time evolution is actually something…
In this letter, we propose a relationship between the so-called Hubble-Lema\^{i}tre constant $H_{0}$ and holographic complexity related to the emergence of spacetime in quantum gravity. Such a result can represent an important step to…