The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous, and conjecturing that this distribution should follow a fractal pattern in perturbed standard cosmologies. This is due to a geometrical effect, appearing when certain types of average densities are calculated along the past light cone. The paper starts reviewing the argument concerning the possibility that the galaxy distribution follows such a scaling pattern, and the premises behind the assumption that the spatial homogeneity of standard cosmology can be observable. Next, it is argued that to discuss observable homogeneity one needs to make a clear distinction between local and average relativistic densities, and showing how the different distance definitions strongly affect them, leading the various average densities to display asymptotically opposite behaviours. Then the paper revisits Ribeiro's (1995: astro-ph/9910145) results, showing that in a fully relativistic treatment some observational average densities of the flat Friedmann model are not well defined at z ~ 0.1, implying that at this range average densities behave in a fundamentally different manner as compared to the linearity of the Hubble law, well valid for z < 1. This conclusion brings into question the widespread assumption that relativistic corrections can always be neglected at low z. It is also shown how some key features of fractal cosmologies can be found in the Friedmann models. In view of those findings, it is suggested that the so-called contradiction between the cosmological principle, and the galaxy distribution forming an unlimited fractal structure, may not exist.Comment: 30 pages, 2 figures, LaTeX. This paper is a follow-up to gr-qc/9909093. Accepted for publication in "General Relativity and Gravitation

Emergence of the pointer basis through the dynamics of correlations

We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we show that these correlations may have a sudden transition from a decay regime to a constant level. This transition characterizes a non-asymptotic emergence of the pointer basis, while the system-apparatus can still be quantum correlated. We provide a formalization of the concept of emergence of a pointer basis in an apparatus subject to decoherence. This contrast of the pointer basis emergence to the quantum to classical transition is demonstrated in an experiment with polarization entangled photon pairs.Comment: 4+2 pgs, 3 figures. Title changed. Revised version to appear on PR

Quantum correlations in a few-atom spin-1 Bose-Hubbard model

We study the thermal quantum correlations and entanglement in spin-1 Bose-Hubbard model with two and three particles. While we use negativity to calculate entanglement, more general non-classical correlations are quantified using a new measure based on a necessary and sufficient condition for zero-discord state. We demonstrate that the energy level crossings in the ground state of the system are signalled by both the behavior of thermal quantum correlations and entanglement