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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…
Motivated by the stability of the electroweak Higgs vacuum we consider the possibility that the Standard Model might work up to large scales between about $10^{10}$ GeV and close to the Planck scale. A plausible scenario is an emergent…
The fully general calculation of the cosmic error on N-point correlation functions and related quantities is presented. More precisely, the variance caused by the finite volume, discreteness, and edge effects is determined for {\em any}…
Astrophysical plasmas in the surrounding of compact objects and subject to intense gravitational and electromagnetic fields are believed to give rise to relativistic regimes. Theoretical and observational evidence suggest that magnetized…
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact,…
We describe a rigorous construction, using matched asymptotic expansions, which establishes under very general conditions that local terrestrial and solar-system experiments will measure the effects of varying `constants' of Nature…
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…
We derive strong observational limits on any possible large-scale spatial variation in the values of physical 'constants' whose space-time evolution is driven by a scalar field. The limits are imposed by the isotropy of the microwave…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
We show that the characteristic sizes of astrophysical and cosmological structures, where gravity is the only overall relevant interaction assembling the system, have a phenomenological relation to the microscopic scales whose order of…
In the context of Einstein gravity, if the null energy condition (NEC) is satisfied, the energy density in expanding space-times always decreases while in contracting space-times the energy density grows and the universe eventually…
Using the Langevin approach and the multiscale technique, a kinetic theory of the time and space nonlocal fluctuations in the collisional plasma is constructed. In local equilibrium a generalized version of the Callen-Welton theorem is…
We develop the formalism to investigate the relation between the evolution of the large-scale (quasi) linear structure and that of the small-scale nonlinear structure in Newtonian cosmology within the Lagrangian framework. In doing so, we…
We introduce a cosmological model in the framework of Generalised Massive Gravity. This theory is an extension of non-linear massive gravity with a broken translation symmetry in the St\"uckelberg space. In a recent work, we showed the…
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…
The equivalence of inertial and gravitational masses is a defining feature of general relativity. Here, we clarify the status of the equivalence principle for interactions mediated by a universally coupled scalar, motivated partly by recent…
The tests of the constancy of the fundamental constants are tests of the local position invariance and thus of the equivalence principle. We summarize the various constraints that have been obtained and then describe the connection between…
The nonassociative generalization of supersymmetry is considered. It is shown that the associator of four supersymmetry generators has the coefficient $\sim \hbar/ \ell_0^2$ where $\ell_0$ is some characteristic length. Two cases are…
We advance the viewpoint that only relevant modes of the vacuum fluctuations, namely, with wavelengths conditioned by the size, homogeneity, geometry and topology of the Universe, do contribute into the cosmological constant. A formula is…