Related papers: Mathematical Models in Isotropic Cosmology
General cosmological models with spinor and scalar fields playing the role of gravitational sources are analyzed. The Noether symmetry approach is taken as a criterion to constrain the undefined potentials and couplings of the generic…
Anisotropic cosmological spacetimes are constructed from spherically symmetric solutions to Einstein's equations coupled to nonlinear electrodynamics and a positive cosmological constant. This is accomplished by finding solutions in which…
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…
In this paper, we consider homogeneous cosmological solutions in the context of the Weyl geometrical scalar-tensor theory. Firstly, we exhibit an anisotropic Kasner type solution taking advantage of some similarities between this theory and…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
We introduce an axiomatic theory of spherical diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context of Art Gallery problems for polyhedra and other…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological constant near the de Sitter equilibrium…
Cosmology of self-interacting three-forms is investigated. The minimally coupled canonical theory can naturally generate a variety of isotropic background dynamics, including scaling, possibly transient acceleration and phantom crossing. An…
We investigate the cosmology of a class of model with noncanonical scalar field and matter in an anisotropic time dependent background. Writing the Einstein Equations in terms of dimensionless dynamical variables appropriately defined for…
In this paper we investigate the asymptotic behavior of the cosmological model based on phantom scalar field on the ground of qualitative analysis of the system of the cosmological model's differential equations and show that as opposed to…
Centre manifold theory is applied to some dynamical systems arising from spatially homogeneous cosmological models. Detailed information is obtained concerning the late-time behaviour of solutions of the Einstein equations of Bianchi type…
In this short note, we define and characterize all the spacetimes admitting observers to whom the cosmic expansion is homogeneous and isotropic and interpret their Einstein's equations.
Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein's field equations where the spatial sections are flat and the source is a non-perfect fluid such that the dissipative terms…
The paper presents results for deriving closed-form analytic solutions of the non-relativistic linear perturbation equations, which govern the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model.…
With the help of our own software package DifEqTools, numerical modeling of the cosmological evolution of a system consisting of an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields, a classical field and a phantom…
We consider the gravitational model with additional spatial dimensions and anisotropic pressure which is nonzero only in these dimensions. Cosmological solutions in this model include accelerated expansion of the Universe at late age of its…
It is given an algorithm to obtain generalized power asymptotic expansions of the solutions of the Einstein equations arising for several homogeneous cosmological models. This allows to investigate their behavior near the initial…
This article gives a conceptual introduction to the topos approach to the formulation of physical theories.
On the basis of a qualitative and numerical analysis of a cosmological model based on an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields -- one classical and one phantom, peculiarities of the behavior of the…