Related papers: Separable sequences in Bianchi I loop quantum cosm…
The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the…
In the present work we show that the widely believed pathology of the non-unitarity of anisotropic quantum cosmological models cannot be a generic problem. We exhibit a non trivial example, a Bianchi-I model with an ultrarelativistic fluid,…
The Gowdy cosmologies provide a suitable arena to further develop Loop Quantum Cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of…
The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so-called quasi-Heisenberg) equations describing an explicit…
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…
We compare two different approaches for quantization of the Bianchi I model: a reduced phase space quantization, in which the isotropic Misner variables is taken as time, and the Vilenkin proposal, in which a semiclassical approximation is…
For the Bianchi type I space-time (vacuum or with a massless scalar field), the loop quantum cosmology bounce can be viewed as a rapid transition between two classical solutions, with a simple transformation rule relating the Kasner…
Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely…
In this paper we report on results in the study of spatially homogeneous cosmological models with elastic matter. We show that the behavior of elastic solutions is fundamentally different from that of perfect fluid solutions already in the…
In the loop quantum cosmology effective dynamics for the vacuum Bianchi type I and type IX space-times, a non-singular bounce replaces the classical singularity. The bounce can be approximated as an instantaneous transition between two…
We present the affine coherent state quantization of the Bianchi I model. As in our previous paper on quantum theory of Friedmann models, we employ a variable associated with a perfect fluid to play a role of clock. Then we deparameterize…
Spherical contours introduced in \cite{SphericalContours} translate the concept of "discontinuity across a branch cut" to Feynman parameter space. In this paper, we further explore spherical contours and connect them to the computation of…
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…
We propose a method to recover the time variable and the classical evolution of the Universe from the minisuperspace wave function of the Wheeler-DeWitt equation. Defining a Hamilton-Jacobi characteristic function $W$ as the imaginary part…
We study the classical and quantum theory of a class of nonlinear differential equations on chronology violating spacetime models in which space consists of finitely many discrete points. Classically, in the linear and weakly nonlinear…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…
Non-singular Bianchi type I solutions are found from the effective action with a superstring-motivated Gauss-Bonnet term. These anisotropic non-singular solutions evolve from the asymptotic Minkowski region, subsequently super-inflate, and…
The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial…
We investigate Bianchi I cosmological model in the theory of a dilatonM field coupled to gravity through a Gauss-Bonnet term. Two type ofM cosmological singularity are distinguished. The former is analogous toM the Einstein gravity…