Related papers: Some integrals ocurring in a topology change probl…
What is the shape of space is a long-standing question in cosmology. In this talk I review recent advances in cosmic topology since it has entered a new era of experimental tests. High redshift surveys of astronomical sources and accurate…
The problem of topology change transitions in quantum gravity is discussed. We argue that the contribution of the Giddings-Strominger wormhole to the Euclidean path integral is pure imaginary. This is checked by two techniques: by the…
A proposal is made for what may well be the most elementary Riemannian spaces which are homogeneous but not isotropic. In other words: a proposal is made for what may well be the nicest symmetric spaces beyond the real space forms, that is,…
The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth…
We prove a converse to well-known results by E. Cartan and J. D. Moore. Let $f\colon M^n_c\to\Q^{n+p}_{\tilde c}$ be an isometric immersion of a Riemannian manifold with constant sectional curvature $c$ into a space form of curvature…
In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and…
We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of…
Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology…
The interest of part of the quantum-gravity community in the possibility of Planck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective,…
The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be…
This paper deals with two aspects of relativistic cosmologies with closed (compact and boundless) spatial sections. These spacetimes are based on the theory of General Relativity, and admit a foliation into space sections S(t), which are…
Quantum effects are expected to modify the cosmological dynamics of the early universe while maintaining some (potentially discrete) notion of space-time structure. In one approach, loop quantum cosmology, current models are shown here to…
We apply topspin network formalism to Loop Quantum Gravity in order to include in the theory the possibility of changes in the topology of spacetime. We apply this formalism to three toy models: with the first, we find that the topology can…
In these two lectures I describe the difficulties one encounters when trying to construct a framework in which to describe topology change in classical general relativity where one sticks to the assumption of an everywhere non-singular…
``One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an…
A bouncing scenario of a flat homogeneous and isotropic universe is explored by using the reconstruction technique for the power-law parametrization of the Hubble parameter in a modified gravity theory with higher-order curvature and trace…
Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early universe. Further, in the context of these theories, it is possible that cosmological phase transitions…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
In the mini-superspace approximation to cosmology, the canonical measure can be used to compute probabilities when a cutoff is introduced in the phase space to regularize the divergent measure. However, the region initially constrained by a…