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In this article it is shown that, Sommerfeld's coefficients for excitonic transitions in quantum wells are determined only with the principle quantum number within the framework of two-dimensional Coulomb potential. This is a consequence of…
The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and the Lorenzian term are thus regularized…
We analyse shear-free spherically symmetric relativistic models of gravitating fluids with heat flow and electric charge defined on higher dimensional manifolds. The solution to the Einstein-Maxwell system is governed by the pressure…
We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the…
We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two…
In quantum field theory the parameters of the vacuum action are subject to renormalization group running. In particular, the ``cosmological constant'' is not a constant in a quantum field theory context, still less should be zero. In this…
The revision of the Author's results with respect to possibility of existence of the so-called Euclidian cycles in cosmological evolution of a system of Higgs scalar fields has been performed. The assumption of non-negativity of the…
We solve Einstein's equation with Robertson-Walker metric as an initial-value problem, using as the source of gravity a Halpern-Huang real scalar field, which was derived from renormalization-group analysis, with a potential that exhibits…
Relativistic field theories with a power law decay in $r^{-k}$ at spatial infinity generically possess an infinite number of conserved quantities because of Lorentz invariance. Most of these are not related in any obvious way to symmetry…
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…
In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on…
On the basis of qualitative analysis of the system of differential equations of the standard cosmological model it is shown that in the case of zero cosmological constant this system has a stable center corresponding to zero values of…
We present an updated analysis of the first-order phase transition associated with symmetry breaking in the early Universe in a classically scale-invariant model extended with a new SU(2) gauge group. Including recent developments in…
In this paper, we investigate the Noether symmetries of a generalized scalar-tensor, Brans-Dicke type cosmological model, in which we consider explicit scalar field dependent couplings to the Ricci scalar, and to the scalar field kinetic…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
Non-minimally coupled scalar field models are well-known for providing interesting cosmological features. These include a late time dark energy behavior, a phantom dark energy evolution without singularity, an early time inflationary…
In these lecture notes I review the theory of the non--linear evolution of cosmological perturbations in a self--gravitating collisionless medium, with vanishing vorticity. The problem is first analyzed in the context of the Newtonian…
We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Thus our approach does not contradict to a rather common opinion that quantum mechanics could not be reduced to…
We study the cosmological dynamics of a class of symmetric teleparallel gravity theories known as ``newer general relativity'' using the methods of dynamical systems, restricted to the case of vacuum solutions with a spatially flat…
We consider a general theory of all possible quadratic, first-order derivative terms of the non-metricity tensor in the framework of Symmetric Teleparallel Geometry. We apply the Noether Symmetry Approach to classify those models that are…