Related papers: Global dynamics of cosmological scalar fields -- P…
I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration form a set that is exhaustive. They never…
In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems…
We consider the problem of critical gravitational collapse of a scalar field in 2+1 dimensions with spherical (circular) symmetry. After surveying all the analytic, continuously self-similar solutions and considering their global structure,…
Continuing the investigation of the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity we study an influence of the cosmological constant on the behaviour of trajectories in…
The paper deals with a dynamical system analysis related to phantom cosmological model . Here gravity is coupled to phantom scalar field having scalar coupling function and a potential. The field equations are reduced to an autonomous…
We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1+3 covariant and 1+3 orthonormal frame notation, and show there exists a series of constraint equations that…
A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…
We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory with a variety of matter terms. For some of these models the standard Painlev\'{e} test is sufficient to demonstrate…
In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a…
We consider a cosmological model with two scalar fields minimally coupled to gravity which have a mixed kinetic term. Hence, Chiral cosmology is included in our analysis. The coupling function and the potential function, which depend on one…
The current status of the recent developments of the second-order gauge-invariant cosmological perturbation theory is reviewed. To show the essence of this perturbation theory, we concentrate only on the universe filled with a single scalar…
We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy…
One possible description for the current accelerated expansion of the universe is quintessence dynamics. The basic idea of quintessence consists of analyzing cosmological scenarios driven by scalar fields. In this work we present some…
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…
We show that several integrable (i.e., exactly solvable) scalar cosmologies considered by Fr\'e, Sagnotti and Sorin (Nuclear Physics \textbf{B 877}(3) (2013), 1028--1106) can be generalized to include cases where the spatial curvature is…
We study a class of scalar field models coupled to impurities in arbitrary spacetime dimensions. The system admits the introduction of a second-order tensor that can be forced to obey an equality, if a first-order differential equation is…
A complete cosmological evolution model of the classical scalar field with a Higgs potential is studied and simulated on a computer without the assumption that the Hubble constant is nonnegative. It is shown that with most initial…
The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature…