Related papers: Dynamical Systems in Cosmology
We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the…
We describe the cosmological dynamics of perfect fluids within the framework of effective field theories. The effective action is a derivative expansion whose terms are selected by the symmetry requirements on the relevant long-distance…
A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a 3-dimensional…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
In this work we compile a few differential equations (ODEs) that arise from the relativistic equations in cosmological models that consider the ``constants'' as scalars functions dependent on time and they are described as perfect as well…
The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states…
In this work we try to understand the late time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe…
Dynamical system methods are used in the study of the stability of spatially flat homogeneous cosmologies within a large class of generalized modified gravity models in the presence of a relativistic matter-radiation fluid. The present…
The late time accelerated expansion of the universe can be realized using scalar fields with given self-interacting potentials. Here we consider a straightforward approach where a three cosmic fluid mixture is assumed. The fluids are…
In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as…
Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems…
A closed set of equations for the evolution of linear perturbations of homogeneous, isotropic cosmological models can be obtained in various ways. The simplest approach is to assume a macroscopic equation of state, e.g.\ that of a perfect…
We use a dynamical system approach to study the cosmological viability of $f(R,\mathcal{G})$ gravity theories. The method consists of formulating the evolution equations as an autonomous system of ODEs, using suitable variables. The…
The study addresses matter-coupled modified gravity, particularly $f (T, \mathcal{T})$ gravity, unveiling distinct formalism. The research further discusses stability analysis, and the dynamical system approach, exploring the dynamics of…
We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
In Friedman-Robertson-Walker flat spacetime, we consider a three fluid cosmological model which contains dark matter, dark energy and baryonic matter in the form of perfect fluid with a barotropic equation of state. Dark matter is taken in…
We study early universe cosmologies derived from a scalar-tensor action containing cosmological constant terms and massless fields. The governing equations can be written as a dynamical system which contains no past or future asymptotic…