Related papers: Dynamical systems approach to G2 cosmology
The flows of phase trajectories of cosmological models based on the vacuum classical Higgs field and their behavior on the Einstein-Higgs surface near singular points of a dynamical system are investigated by numerical simulation. The…
A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $\gamma -$law…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
We consider the evolution of a flat Friedmann-Roberstson-Walker Universe in a higher derivative theories, including $\alpha R^{2}$ terms to the Einstein-Hilbert action in the presence of a variable gravitational and cosmological constants.…
In this contribution we further study the classical disordered p=2 spherical model with Hamiltonian dynamics, or in integrable systems terms, the Neumann model, in the infinite size limit. We summarise the asymptotic results that some of us…
In this paper we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator $\hat{F}$ and result in different…
We apply dynamical systems techniques to investigate cosmological models inspired in scalar-tensor theories written in the Einstein frame. We prove that if the potential and the coupling function are sufficiently smooth functions, the…
We use Fuchsian Reduction to study the behavior near the singularity of a class of solutions of Einstein's vacuum equations. These solutions admit two commuting spacelike Killing fields like the Gowdy spacetimes, but their twist does not…
Dynamical systems methods are used to investigate cosmological model with non-minimally coupled scalar field. Existence of an asymptotically unstable de Sitter state distinguishes values of the non-minimal coupling constant parameter…
The dynamical aspect of accelerating cosmological model has been studied in this paper in the context of modified symmetric teleparallel gravity, the $f(Q)$ gravity. Initially, we have derived the dynamical parameters for two well known…
Solutions of Einstein vacuum equations, for a static pseudospherically symmetric system, are presented. They describe a naked singularity and a singular solution with many resemblances to the Schwartzschild solution but with two major…
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 dynamical realisation of the equation of state $p +\rho =0$ is studied. A non-pathological dynamics for the perturbations of such a system mimicking a dynamical cosmological constant (DCC) requires to go beyond the perfect fluid…
We consider the problem of building inhomogeneous cosmological models in scalar-tensor theories of gravity. This starts by splitting the field equations of these theories into constraint and evolution equations, and then proceeds by…
The existence of static and axially symmetric regions in a Friedman-Lemaitre cosmology is investigated under the only assumption that the cosmic time and the static time match properly on the boundary hypersurface. It turns out that the…
We use a dynamical systems analysis to investigate the future behaviour of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a non-interacting perfect fluid. The stability of the equilibrium…
We investigate the asymptotic damping of a perturbation around inhomogeneous stable stationary states of the Vlasov equation in spatially multi-dimensional systems. We show that branch singularities of the Fourier-Laplace transform of the…
Utilizing the autonomous system of ordinary differential equations derived in arXiv:1809.01458 to define the evolution, we further investigate a class of cosmological models within an Einstein-aether gravitational framework by introducing a…