Related papers: Comparing the dynamics of diagonal and general Bia…
The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian…
We study the dynamics of the vacuum Bianchi IX model with timelike singularity and compare it with the dynamics of the Bianchi IX model with cosmological singularity. We show that differences in the signs of some terms in the set of…
We present the analyses of the asymptotic evolution of the general Bianchi IX spacetime using Hamiltonian formulation. The dynamics reveals the existence of special structures, which we call wiggles, in the physical phase space. The wiggles…
Half a century ago, Belinsky and Khalatnikov proposed a generic solution of the Einstein equations near their cosmological singularity, based on a generalization of the homogeneous model of Bianchi type IX. Consideration of the evolution of…
The dynamics of the Bianchi IX cosmological model with minimally coupled massive real scalar field is studied. The possibility of non-singular transition from contraction to expansion is shown. A set of initial conditions that lead to…
In this work we study the dynamics of the axisymmetric Bianchi IX cosmological model with a term of quantum potential added. As it is well known this class of Bianchi IX models are homogeneous and anisotropic with two scale factors, $A(t)$…
In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type…
We examine the Hamiltonian dynamics of bouncing Bianchi IX cosmologies in Ho\v{r}ava-Lifshitz gravity. The $6$-dim phase space presents two critical points, one asymptotic de Sitter attractor at infinity and a $2$-dim invariant plane. We…
The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of…
We examine the dynamics of a Bianchi IX model on a 4-dim brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. Einstein's equations on the brane reduces to a 6-dim Hamiltonian dynamical system with…
The dynamics of the general Bianchi IX spacetime, near the gravitational singularity, underlies the Belinskii, Khalatnikov and Lifshitz scenario. Asymptotically, near the singularity, the oscillations of the directional scale factors…
We consider some aspects of the global evolution problem of Hamiltonian homogeneous, anisotropic cosmologies derived from a purely quadratic action functional of the scalar curvature. We show that models can isotropize in the positive…
We show that the complex dynamics of the general Bianchi IX universe in the vicinity of the spacelike singularity can be approximated by a simplified system of equations. Our analysis is mainly based on numerical simulations. The properties…
We study the cosmological dynamics of non-minimally coupled matter models using the Brown's variational approach to relativistic fluids in General Relativity. After decomposing the Ricci scalar into a bulk and a boundary term, we construct…
Making use of the $1 + 3$ covariant formalism, we show explicitly the effect that nonmetricity has on the dynamics of the universe. Then, using the Dynamical System Approach, we analyze the evolution of Bianchi type-I cosmologies within the…
All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them…
In this paper we study the dynamics of {\it orthogonal spatially homogeneous} Bianchi cosmologies in $R^n$-gravity. We construct a compact state space by dividing the state space into different sectors. We perform a detailed analysis of the…
We investigate the dynamics of closed FRW universe and anisotropic Bianchi type-IX universe characterized by two scale factors in a gravity theory including a higher curvature (Gauss-Bonnet) term. The presence of the cosmological constant…
In this paper we present a framework in which the relational description of General Relativity can be used to smoothly continue cosmological dynamical systems through the Big Bang without invoking quantum gravity effects. Cosmological…
Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The…