Related papers: Cosmological dynamical systems
A basic modern picture of the universe is given here. The lectures start from the historical ideas of a static universe. Then I move on to Newtonian cosmology and derive the main cosmological equations in the framework of Newtonian…
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…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
An introduction to solutions of the Einstein equations defining cosmological models with accelerated expansion is given. Connections between mathematical and physical issues are explored. Theorems which have been proved for solutions with…
We discussed the dynamics of cosmological models in which the cosmological constant term is a time dependent function through the scale factor $a(t)$, Hubble function $H(t)$, Ricci scalar $R(t)$ and scalar field $\phi(t)$. We considered…
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum…
Using the dynamical systems approach together with the cosmographic parameters, we present a model-independent dynamical system formulation for cosmology in f(R) gravity. The formulation is model-independent in the sense that one needs to…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
This article briefly summarizes the increasingly precise observational estimates of the cosmological parameters. After three years on the stump, the Lambda-CDM model is still the leading candidate. Although the Universe is expanding, our…
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario derived from the solution…
For most of its history, cosmology was a qualitatively constrained discourse on the universe, shaped by limited observational access and the absence of global dynamical laws. This situation has changed decisively in recent decades. Modern…
I give a geometric construction of certain first order natural dynamical observables in multifield cosmological models with arbitrary target space topology and discuss a system of related dynamical approximations and regimes for such…
A complete model of cosmological evolution of a classical scalar field with the Higgs potential is studied and simulated on a computer without assumption that the Hubble constant is nonnegative. The corresponding dynamical system is…
Motivated by the recent observations for the cosmic acceleration and the suitable evolution of the Universe provided an interaction (decay of dark energy to matter) is incorporated in a cosmological model, we study the cosmological…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
Dynamical aspects of cosmological model in an extended gravity theory have been investigated in the present work. We have adopted a simplified approach to obtain cosmic features, which in fact requires more involved calculations. A…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
This paper presents a systematic literature review focusing on the application of machine learning techniques for deriving observational constraints in cosmology. The goal is to evaluate and synthesize existing research to identify…
This is a review article for The Review of Particle Physics 2010 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the beginning of 2010. Topics included are Parametrizing the Universe;…
In this work, we use an observational approach and dynamical system analysis to study the cosmological model recently proposed by Saridakis (2020), which is based on the modification of the entropy-area black hole relation proposed by…