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A detailed qualitative analysis and numerical modeling of the evolution of cosmological models based on nonlinear classical and phantom scalar fields with self-action are performed. Complete phase portraits of the corresponding dynamical…
Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions, a cosmological model based on a one-component statistical system of doubly scalar charged degenerate fermions interacting…
Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time…
A mathematical model of the cosmological evolution of statistical systems of scalarly charged particles with Higgs scalar interaction is formulated and investigated. Examples are given of numerical modeling of such systems, revealing their…
We consider a scalar field with a negative kinetic term minimally coupled to gravity. We obtain an exact non-static spherically symmetric solution which describes a wormhole in cosmological setting. The wormhole is shown to connect two…
We investigate cosmological models with a free scalar field and a viscous fluid. We find exact solutions for a linear and nonlinear viscosity pressure. Both yield singular and bouncing solutions. In the first regime, a de Sitter stage is…
In this work we consider the evolution of a massive scalar field in cylindrically symmetric space-times. Quasinormal modes have been calculated for static and rotating cosmic cylinders. We found unstable modes in some cases. Rotating as…
Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the…
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 use the phase plane analysis technique of Madsen and Ellis to consider a universe with a true cosmological constant as well as a cosmological "constant" that is decaying. Time symmetric dynamics for the inflationary era allows eternally…
We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space. We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric. The metric in the ensemble is used to measure a…
A mathematical model is constructed for the evolution of spherical perturbations in a cosmological one-component statistical system of completely degenerate scalarly charged fermions with a scalar Higgs interaction. A complete system of…
The asymptotic behaviour of a family of inhomogeneous scalar field cosmologies with exponential potential is studied. By introducing new variables we can perform an almost complete analysis of the evolution of these cosmologies. Unlike the…
We investigate the late-time evolution of the Universe within a cosmological model in which dark matter and dark energy are identified with two interacting scalar fields. Using methods of qualitative analysis of dynamical systems, we…
Cosmological models often contain scalar fields, which can acquire global nonzero expectation values that change with the comoving time. Among the possible consequences of these scalar-field backgrounds, an accelerated cosmological…
Spatially homogeneous cosmological models with a positive cosmological constant are investigated, using dynamical systems methods. We focus on the future evolution of these models. In particular, we address the question whether there are…
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…
We study evolution of cosmological models filled with the scalar field and barotropic matter. We consider the scalar field minimally and non-minimally coupled to gravity. We demonstrated the growth of degree of complexity of evolutional…
We perform a detailed analysis for the dynamics of Chiral cosmology in a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe with a mixed potential term. The stationary points are categorized in four families. Previous results…
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…