Distinguishing Marks of Simply-connected Universes

A statistical quantity suitable for distinguishing simply-connected Robertson-Walker (RW) universes is introduced, and its explicit expressions for the three possible classes of simply-connected RW universes with an uniform distribution of matter are determined. Graphs of the distinguishing mark for each class of RW universes are presented and analyzed.There sprout from our results an improvement on the procedure to extract the topological signature of multiply-connected RW universes, and a refined understanding of that topological signature of these universes studied in previous works.Comment: 13 pages, 4 figures, LaTeX2e. To appear in Int. J. Mod. Phys. D (2000

The exit-time problem for a Markov jump process

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.Comment: 15 pages, 7 figure

Can We See the Shape of the Universe?

This is a written version of a talk given at the Fifth Friedmann Seminar on recent work in Observational Cosmic Topology done in partial collaboration with Armando Bernui. We address three relevant questions related to the search for the size and shape of our Universe: (i) How do the actual observation of multiple images of certain cosmic objects, e.g. galaxy clusters, constrain the possible models for the shape of our Universe?, (ii) What kind of predictions can be done once a pair of cosmic objects have been identified to be topological images related by a translation?, and (iii) Is it possible to determine if two regions of space are topologically identified, even when distortions on the distributions of cosmic sources due to observational limitations are not negligible? We give examples answering the first two questions using the suggestion of Roukema and Edge that the clusters RXJ 1347.5-1145 and CL 09104+4109 might be topological images of the Coma cluster. For the third question, we suggest a method based on the analysis of PSH's noise correlations which seems to give a positive answer.Comment: 6 pages, latex2e, contribution to the 5th Alexander Friedmann Seminar on Gravitation and Cosmology, to appear in Int. J. Mod. Phys. A (2002). Macros: ws-ijmpa.cl

Wave function statistics at the symplectic 2D Anderson transition: bulk properties

The wavefunction statistics at the Anderson transition in a 2d disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents ($\alpha_0{=}2.172\pm 0.002, \tau_2{=}1.642\pm 0.004$), we report three qualitative results: (i) the anomalous dimensions are invariant under $q\to (1-q)$ which is in agreement with a recent analytical prediction and supports the universality hypothesis. (ii) The multifractal spectrum is not parabolic and therefore differs from behavior suspected, e.g., for (integer) quantum Hall transitions in a fundamental way. (iii) The critical fixed point satisfies conformal invariance.Comment: 4 pages, 3 figure

Abundance of Ground States with Positive Parity

We investigate analytically and numerically a random-matrix model for m fermions occupying l1 single-particle states with positive parity and l2 single-particle states with negative parity and interacting through random two-body forces that conserve parity. The single-particle states are completely degenerate and carry no further quantum numbers. We compare spectra of many-body states with positive and with negative parity. We show that in the dilute limit, ground states with positive and with negative parity occur with equal probability. Differences in the ground-state probabilities are, thus, a finite-size effect and are mainly due to different dimensions of the Hilbert spaces of either parity.Comment: 12 pages, 1 figur

GRBs and the 511 keV emission of the Galactic bulge

We consider the phenomenology of the 511 keV emission in the Galactic bulge, as recently observed by INTEGRAL, and propose a model is which the positrons are produced by gamma-ray bursts (GRB) associated with mini starbursts in the central molecular zone (CMZ). We show that the positrons can easily diffuse across the bulge on timescales of about 10^7 yr, and that their injection rate by GRBs is compatible with the observed fluxes if the mean time between two GRBs in the bulge is about 8 10^4 yr x E_GRB_51. We also explain the low disk-to-bulge emission ratio by noting that positrons from GRBs in the Galactic disk should annihilate on timescales of < 10^4 yr in the dense shell of the underlying supernova remnant, after the radiative transition, while the remnants of GRBs occurring in the hot, low-density medium produced by recurrent starbursts in the CMZ become subsonic before they can form a radiative shell, allowing the positrons to escape and fill the whole Galactic bulge. If the mean time between GRBs is smaller than 10^4 E_51 yr, INTEGRAL should be able to detect the (localized) 511 keV emission associated with one or a few GRB explosions in the disk.Comment: 6 pages, accepted for publication in A&

Observational constraints on modified gravity models and the Poincar\'e dodecahedral topology

We study the constraints that spatial topology may place on the parameters of models that account for the accelerated expansion of the universe via infrared modifications to general relativity, namely the Dvali-Gabadadze-Porrati braneworld model as well as the Dvali-Turner and Cardassian models. By considering the Poincar\'e dodecahedral space as the circles-in-the-sky observable spatial topology, we examine the constraints that can be placed on the parameters of each model using type Ia supernovae data together with the baryon acoustic peak in the large scale correlation function of the Sloan Digital Sky Survey of luminous red galaxies and the Cosmic Microwave Background Radiation shift parameter data. We show that knowledge of spatial topology does provide relevant constraints, particularly on the curvature parameter, for all models.Comment: Revtex4, 10 pages, 1 table, 12 figures; version to match the one to be published in Physical Review