Related papers: Absence of the Kasner singularity in the effective…
The dynamics of solutions of the Einstein-Vlasov system with Bianchi I symmetry is discussed in the case of massive or massless particles. It is shown that in the case of massive particles the solutions are asymptotic to isotropic dust…
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…
General Relativity predicts that the spacetime near a cosmological singularity undergoes an infinite number of chaotic oscillations between different Kasner epochs with rapid transitions between them. This so-called BKL behaviour persists…
We study the anisotropic Bianchi I loop quantum cosmology in 2+1 dimensions. Both the $\mubar$ and $\mubar'$ schemes are considered in the present paper and the following expected results are established: (i) the massless scalar field again…
We analyse the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach,…
We discuss the question of time in a Bianchi I quantum cosmology in the framework of singularity avoidance. We show that time parameters fall into two distinct classes, that are such that the time development of the wave function either…
We analyze the dynamics of a class of cosmological solutions of the Einstein-Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively…
We investigate a cosmological model with a big-brake singularity in the future: while the first time derivative of the scale factor goes to zero, its second time derivative tends to minus infinity. Although we also discuss the classical…
Quantum states of the diagonal Bianchi type IX model with negative cosmological constant $\Lambda$ are obtained by transforming the Chern-Simons solution in Ashtekar's variables to the metric representation. We apply our method developed…
We investigate the behaviour on approach to the initial singularity in higher-order extensions of general relativity by finding exact cosmological solutions for a wide class of models in which the Lagrangian is allowed to depend nonlinearly…
In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a…
The non-diagonal Bianchi models are studied in the loop framework for their classical and quantum formulation. The expressions of the Ashtekar-Barbero-Immirzi variables and their properties are found to provide a loop quantization of these…
We study the generic resolution of strong singularities in loop quantized effective Bianchi-IX spacetime in two different quantizations - the connection operator based `A' quantization and the extrinsic curvature based `K' quantization. We…
Methods of dynamical systems analysis are used to show rigorously that the presence of a magnetic field orthogonal to the two commuting Killing vector fields in any spatially homogeneous Bianchi type VI_0 vacuum solution to Einstein's…
Due to the numerical complexities of studying evolution in an anisotropic quantum spacetime, in comparison to the isotropic models, the physics of loop quantized anisotropic models has remained largely unexplored. In particular, robustness…
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a…
In the present paper we generalize the original work of C.W. Misner \cite{M69q} about the quantum dynamics of the Bianchi type IX geometry near the cosmological singularity. We extend the analysis to the generic inhomogeneous universe by…
We study homogeneous cosmological models in formulations of general relativity with cosmological constant based on a (complexified) connection rather than a spacetime metric, in particular in a first order theory obtained by integrating out…
It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded…
It is well known that a closed universe with a minimally coupled massive scalar field always collapses to a singularity unless the initial conditions are extremely fine tuned. We show that the corrections to the equations of motion for the…