Zdzisław A. Golda

Structurally stable approximations to Friedmann—Lemaître world models

Friedmann—Lemaître cosmology is briefly reviewed in terms of dynamical systems. It is demonstrated that in certain cases bulk viscosity dissipation structurally stabilizes Friedmann—Lemaître solutions. It turns out that, for A=0, there are structurally stable solutions if ξ~ε1/2, where ξ is the bulk viscosity coefficient. For A≠0 structurally stable solutions are essentially those with ξ=const. The role of structural stability in physics and cosmology is shortly discussed.

Dispersion of density waves in the radiation-dominated universe with positive cosmological constant

Density perturbations in the flat (K = 0) Robertson–Walker universe with radiation (p = e/3) and positive cosmological constant (Λ > 0) are investigated. The phenomenon of dispersion of acoustic waves on Λ is discussed.

Evolution of density perturbations in a realistic universe

Prompted by the recent more precise determination of the basic cosmological parameters and growing evidence that the matter-energy content of the universe is now dominated by dark energy and dark matter we present the general solution of the equation that describes the evolution of density perturbations in the linear approximation. It turns out that as in the standard CDM model the density perturbations grow very slowly during the radiation dominated epoch and their amplitude increases by a factor of about 4000 in the matter and later dark energy dominated epoch of expansion of the universe.

Dynamics of the D-dimensional FRW cosmological models within the superstring generated gravity model

We study the dynamics of the generalizedD-dimensional (D = 1+3+d) Friedman-Robertson-Walker (FRW) cosmological models in the framework of an extended gravity theory obtained by adding the Gauss-Bonnet term to the standard Einstein-Hilbert action. In our discussion we extensively use methods of dynamical systems. We consider models filled in with a perfect fluid obeying the equation of statep=(γ−1)ρ and vacuum but non-flat models. We present a detailed analysis of the ten dimensional model and in particular we study the vacuum case. Several phase portraits show how the evolution of this model depends on the parameterγ.

On integrability of the Szekeres system. I

The Szekeres system is a four-dimensional system of first-order ordinary differential equations with nonlinear but polynomial (quadratic) right-hand side. It can be derived as a special case of the Einstein equations, related to inhomogeneous and nonsymmetrical evolving spacetime. The paper shows how to solve it and find its three global independent first integrals via Darboux polynomials and Jacobi’s last multiplier method. Thus the Szekeres system is completely integrable. Its two-dimensional subsystem is also investigated: we present its solutions explicitly and discuss its behaviour at infinity.

A field theory approach to cosmological density perturbations

Abstract Adiabatic perturbations propagate in the expanding universe like scalar massless fields in some effective Robertson–Walker space–time.

Acoustics of early universe—Lifshitz versus gauge-invariant theories

Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express the metric and density corrections in their exact forms and discuss their acoustic character.

Every timelike geodesic in anti-de Sitter spacetime is a circle of the same radius

We refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti--de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by

Symbolic tensor calculus ‒ functional and dynamic approach

\Lambda

Acoustics of the early universe: flat versus open universe models

, lying on a Euclidean two--plane. Then we outline an alternative proof for