On the possible role of massive neutrinos in cosmological structure formation

In addition to the problem of galaxy formation, one of the greatest open questions of cosmology is represented by the existence of an asymmetry between matter and antimatter in the baryonic component of the Universe. We believe that a net lepton number for the three neutrino species can be used to understand this asymmetry. This also implies an asymmetry in the matter-antimatter component of the leptons. The existence of a nonnull lepton number for the neutrinos can easily explain a cosmological abundance of neutrinos consistent with the one needed to explain both the rotation curves of galaxies and the flatness of the Universe. Some propedeutic results are presented in order to attack this problem.Comment: RevTeX4, 25 pages, 5 figures, to appear in the "Proceedings of the Xth Brazilian School of Cosmology and Gravitation", M. Novello, editor, AIP, in pres

Algorithmic statistics revisited

The mission of statistics is to provide adequate statistical hypotheses (models) for observed data. But what is an "adequate" model? To answer this question, one needs to use the notions of algorithmic information theory. It turns out that for every data string $x$ one can naturally define "stochasticity profile", a curve that represents a trade-off between complexity of a model and its adequacy. This curve has four different equivalent definitions in terms of (1)~randomness deficiency, (2)~minimal description length, (3)~position in the lists of simple strings and (4)~Kolmogorov complexity with decompression time bounded by busy beaver function. We present a survey of the corresponding definitions and results relating them to each other

Non-Singular Bouncing Universes in Loop Quantum Cosmology

Non-perturbative quantum geometric effects in Loop Quantum Cosmology predict a $\rho^2$ modification to the Friedmann equation at high energies. The quadratic term is negative definite and can lead to generic bounces when the matter energy density becomes equal to a critical value of the order of the Planck density. The non-singular bounce is achieved for arbitrary matter without violation of positive energy conditions. By performing a qualitative analysis we explore the nature of the bounce for inflationary and Cyclic model potentials. For the former we show that inflationary trajectories are attractors of the dynamics after the bounce implying that inflation can be harmoniously embedded in LQC. For the latter difficulties associated with singularities in cyclic models can be overcome. We show that non-singular cyclic models can be constructed with a small variation in the original Cyclic model potential by making it slightly positive in the regime where scalar field is negative.Comment: Minor changes and one figure added to improve presentation. References added. To appear in Physical Review

Physical constants and the Gurzadyan-Xue formula for the dark energy

We consider cosmological implications of the formula for the dark energy density derived by Gurzadyan and Xue which predicts a value fitting the observational one. Cosmological models with varying by time physical constants, namely, speed of light and gravitational constant and/or their combinations, are considered. In one of the models, for example, vacuum energy density induces effective negative curvature, while another one has an unusual asymptotic. This analysis also explicitely rises the issue of the meaning and content of physical units and constants in cosmological context.Comment: version corrected to match the one to appear in Modern Physics Letters

Algorithmic statistics: forty years later

Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a "good model" is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad ("non-stochastic") data appear "in real life"? Another, more technical motivation comes from algorithmic information theory. In this theory a notion of complexity of a finite object (=amount of information in this object) is introduced; it assigns to every object some number, called its algorithmic complexity (or Kolmogorov complexity). Algorithmic statistic provides a more fine-grained classification: for each finite object some curve is defined that characterizes its behavior. It turns out that several different definitions give (approximately) the same curve. In this survey we try to provide an exposition of the main results in the field (including full proofs for the most important ones), as well as some historical comments. We assume that the reader is familiar with the main notions of algorithmic information (Kolmogorov complexity) theory.Comment: Missing proofs adde

Quantum Geometry and its Implications for Black Holes

General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will provide a more complete, non-singular extension which, however, was difficult to verify in the absence of a quantum theory of gravity. By now there are several candidates which show essential hints as to what a quantum theory of gravity may look like. In particular, loop quantum gravity is a non-perturbative formulation which is background independent, two properties which are essential close to a classical singularity with strong fields and a degenerate metric. In cosmological and black hole settings one can indeed see explicitly how classical singularities are removed by quantum geometry: there is a well-defined evolution all the way down to, and across, the smallest scales. As for black holes, their horizon dynamics can be studied showing characteristic modifications to the classical behavior. Conceptual and physical issues can also be addressed in this context, providing lessons for quantum gravity in general. Here, we conclude with some comments on the uniqueness issue often linked to quantum gravity in some form or another.Comment: 16 pages, Plenary talk at ``Einstein's Legacy in the New Millenium,'' Puri, India, December 200

GRBs and the thermalization process of electron-positron plasmas

We discuss the temporal evolution of the pair plasma created in Gamma-Ray Burst sources. A particular attention is paid to the relaxation of the plasma into thermal equilibrium. We also discuss the connection between the dynamics of expansion and the spatial geometry of the plasma. The role of the baryonic loading parameter is emphasized.Comment: 4 pages, 3 figures, in the Proceedings of the "Gamma Ray Bursts 2007" meeting, November 5-9, 2007, Santa Fe, New Mexico, US

Coordinate time dependence in Quantum Gravity

The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group averaging method to solve constraints one can nevertheless introduce a classical coordinate time into the quantum theory, and use it to investigate the way a semiclassical continuous description emerges from discrete quantum evolution. Applying this technique to test effective classical equations of loop cosmology and their implications for inflation and bounces, we show that the effective semiclassical theory is in good agreement with the quantum description even at short scales.Comment: 35 pages, 17 figure. Revised version. To appear in Phys. Rev.