Related papers: The cosmological billiard attractor
Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scalar fields and multiple exponential potential is considered. The dynamics of the model near the singularity is reduced to a billiard on the…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
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…
Belinski, Khalatnikov and Lifshitz (BKL) pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a space-like singularity. We show how the use of a…
In this paper, we describe the dynamics of a Bianchi Type V vacuum universe with an arbitrary cosmological constant. We begin by using an orthonormal frame approach to write Einstein's field equations as a coupled system of first-order…
One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular…
Belinskii, Khalatnikov, and Lifshitz (BKL) conjectured that the description of the asymptotic behavior of a generic solution of Einstein equations near a spacelike singularity could be drastically simplified by considering that the time…
In this paper, we analyse the Einstein and Einstein-Maxwell billiards for all spatially homogeneous cosmological models corresponding to 3 and 4 dimensional real unimodular Lie algebras and provide the list of those models which are chaotic…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
We present a heuristic analysis of the dynamics of general solutions to the Einstein Field Equations which highlights the possibility that such systems could possess a degree of unpredictability stronger than that which characterises…
We consider two nested billiards in $\mathbb R^d$, $d\geq3$, with $C^2$-smooth strictly convex boundaries. We prove that if the corresponding actions by reflections on the space of oriented lines commute, then the billiards are confocal…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
We study locally spatially homogeneous solutions of the Einstein-Vlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic…
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 study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally…
We study the early-time behavior of isotropic and homogeneous solutions in vacuum as well as radiation-filled cosmological models in the full, effective, four dimensional gravity theory with higher derivatives. We use asymptotic methods to…
We study cosmological models using dynamical systems and averaging methods, encompassing flat and open FLRW geometries as well as the LRS Bianchi types I, III, and V. Under mild regularity and frequency-scaling assumptions, we obtain a…
The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the…
The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant $\Lambda$ is zero. The resulting framework lies at the foundation of research in diverse…
A study of a complete cosmological model based on an asymmetric scalar doublet represented by the classical and phantom scalar Higgs fields is carried out. At the same time, the assumption about the nonnegativity of the expansion rate of…