Related papers: Global dynamics of the mixmaster model
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity,…
A powerful result in theoretical cosmology states that a subset of anisotropic Bianchi models can be seen as the homogeneous limit of (standard) linear cosmological perturbations. Such models are precisely those leading to Friedmann…
We study some aspects of dynamical compactification scenario where stabilisation of extra dimensions occurs due to presence the Gauss-Bonnet term and non-zero spatial curvature. In the framework of the model under consideration there exists…
Using a qualitative analysis based on the Hamiltonian formalism and the orthonormal frame representation we investigate whether the chaotic behaviour which occurs close to the initial singularity is still present in the far future of…
We investigate static, spherically symmetric solutions in gravitational theories which have limited curvature invariants, aiming to remove the singularity in the Schwarzschild space-time. We find that if we only limit the Gauss-Bonnet term…
In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein's equations consisting in a ($N+2$)-dimensional static and hyperplane symmetric perfect fluid satisfying the…
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…
Homogeneous, nearly-isotropic Bianchi cosmological models are considered. Their time evolution is expressed as a complete set of non-interacting linear modes on top of a Friedmann-Robertson-Walker background model. This connects the…
A new class of a spatially homogeneous and anisotropic Bianchi type-I cosmological models of the universe for perfect fluid distribution within the framework of scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett.…
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 investigate the quantum evolution of the metric operators for Bianchi-Type I model universes in the Heisenberg picture in order to remove the need to consider the wave function of the universe and interpret its "spin" variables. The…
The primary aim of this work is to explore feasible bouncing cosmological solutions in the framework of $f(\mathcal{Q}, \mathcal{C})$ gravity, where $\mathcal{Q}$ denotes non-metricity and $\mathcal{C}$ indicates the boundary term. To…
We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations…
We investigate classically non-singular bounces caused by dark energy. In the presence of positive spatial curvature, vacuum energy, either in the form of a cosmological constant or a scalar field potential, allows for an open set of…
We derive transition rules for Kasner exponents in bouncing Bianchi I models with generic perfect fluid matter fields for a broad class of modified gravity theories where cosmological singularities are resolved and replaced by a…
We consider a five dimensional vacuum cosmology with Bianchi type-IX spatial geometry and an extra non-compact coordinate. Finding a new class of solutions, we examine and rule out the possibility of deterministic chaos. We interpret this…
Previous studies \cite{berger98a} have provided strong support for a local, oscillatory approach to the singularity in U(1) symmetric, spatially inhomogeneous vacuum cosmologies on $T^3 \times R$. The description of a vacuum Bianchi type…
In the context of the Loop Quantum Cosmology we have analysed the holonomy correction to the classical evolution of the simplified Bianchi I model in the presence of vector fields. For the Universe dominated by a massive vector field or by…
The q-models are scenarios that may explain the smallness of the cosmological constant [1]-[7]. The vacuum in these theories is presented as a self-sustainable medium and include a new degree of freedom, the q-variable, which stablish the…
We analyze the dynamics of the Bianchi I model in the presence of stiff matter, an ultrarelativistic component and a small negative cosmological constant. We quantize this model in the framework of the polymer quantum mechanics, in order to…