Related papers: Dynamics of compact homogeneous universes
We introduce the notion of domains with uniform squeezing property, study various analytic and geometric properties of such domains and show that they cover many interesting examples, including Teichmuller spaces and Hermitian symmetric…
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…
We construct several new examples of homogeneous domains in complex space that do not have bounded realisations. They are equivalent to tubes over affinely homogeneous domains in real space and have a real-analytic everywhere Levi…
We review the evolution of a spatially homogeneous and isotropic universe described by a Friedmann-Robertson-Walker spacetime filled with a collisionless, neutral, simple, massive gas. The gas is described by a one-particle distribution…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature $|\operatorname{sec}|\leq 1$. Moreover, we show that the set of geometric models is compact in the…
In this brief note we aim to provide, through a well known class of singular densities in harmonic analysis, a simple approach to the fact that the homogeneity of the universe on scales of the order of a hundred millions light years is…
The effective dynamics of loop quantum gravity for marginally bound Lema\^itre-Tolman-Bondi spacetimes predict that the big-bang singularity is resolved and replaced by a cosmic bounce. Numerics show that these effective dynamics also…
We consider a particular example of dynamical compactification of an anisotropic 7+1 dimensional Universe in Einstein - Gauss - Bonnet gravity. Starting from rather general totally anisotropic initial conditions a Universe in question…
We apply CGHS-type dilaton gravity model to (1+1)-dimensional cosmological situations. First the behavior of a compact 1-dimensional universe (i.e. like a closed string) is classified on the assumption of homogeneity of universe. Several…
In an earlier paper of the authors it was shown that the sheaf theoretically based recently developed abstract differential geometry of the first author can in an easy and natural manner incorporate singularities on arbitrary closed nowhere…
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…
We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…
We find exact solutions in five dimensional inhomogeneous matter dominated model with a varying cosmological constant. Adjusting arbitrary constants of integration one can also achieve acceleration in our model. Aside from an initial…
This paper reviews the dynamics of an isotropic and homogeneous cosmological scalar field. A general approach to the solution of the Einstein-Klein-Gordon equations is developed, which does not require slow-roll or other approximations.…
Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the…
We discuss the inhomogeneous multidimensional mixmaster model in view of appearing, near the cosmological singularity, a scenario for the dimensional compactification in correspondence to an 11-dimensional space-time. Our analysis…
In this note we consider compact homomorphisms and endomorphisms between various Dales-Davie algebras. In particular, we obtain fairly complete results when the underlying set is the disc or the unit circle. Comparable results when the…
We study the possibility that a generalised real scalar field minimally coupled to gravity could explain both the galactic and the cosmological dark components of the universe. Within the framework of Einstein's Relativity we model static…
The dynamics of homogeneous Robertson--Walker cosmological models with a self-interacting scalar field source is examined here in full generality, requiring only the scalar field potential to be bounded from below and divergent when the…