International Journal of Modern Physics A

The aim of the lectures in this paper is to introduce some basic problems arising in gravitation and modern cosmology. All along the discussion the guiding theme is provided by the phenomenological and theoretical properties of the Cosmic Microwave Background (CMB). These lectures have been prepared for a regular PhD course of the University of Milan-Bicocca.

I discuss fundamental limits placed on information and information processing by gravity. Such limits arise because both information and its processing require energy, while gravitational collapse (formation of a horizon or black hole) restricts the amount of energy allowed in a finite region. Specifically, I use a criterion for gravitational collapse called the hoop conjecture. Once the hoop conjecture is assumed a number of results can be obtained directly: the existence of a fundamental uncertainty in spatial distance of order the Planck length, bounds on information (entropy) in a finite region, and a bound on the rate of information processing in a finite region. In the final section I discuss some cosmological issues, related to the total amount of information in the universe, and note that almost all detailed aspects of the late universe are determined by the randomness of quantum outcomes. This paper is based on a talk presented at a 2007 Bellairs Research Institute (McGill University) workshop on black holes and quantum information.

Size and position of rapidity window dependence of charge fluctuations and correlations are studied by PYTHIA and RQMD models for hadron–hadron and nucleus–nucleus collisions respectively. The results show that all the measures for charge fluctuations and correlations depend on the size of central rapidity windows and most of them depend on the position of the rapidity windows, which is not expected. Only charge balance function in hadron–hadron collisions is independent of the position of rapidity window, i.e. boost-invariant, in consistent with corresponding experimental data, while charge fluctuations measured by D(Q) is not boost-invariant in contrast to the experimental data. The measures for three kind of charge correlations (R₊₊, R_--, R_+-) show a good account for the behavior of charge correlations and global charge conservation in longitudinal phase space in both PYTHIA and RQMD.

Recently the authors of arXiv:hep-ph/0510321 propose a GUT model for fermion masses and mixings with spontaneously broken S₃ discrete flavor symmetry, where S₃ is the permutation group of three objects. The S₃ breaking pattern in the quark sector is not studied and need further investigation. Since in such a model the number of free parameters is greater than the number of experimental observables, an analytical fit of all the parameters is impossible. To go forward with the model building and to deal with this problem we have used a statistical analysis. We have found that S₃ is totally broken and the up-type quarks matrix is approximatively diagonal while down-type quarks matrix is not symmetric and it is parametrized by three couplings, g^d, and . It has been found that is slightly smaller than g^d = 1 and it is of order one, while where λ is the Cabibbo angle. An analytical study of the dependence of V_cb and V_ub from the couplings and is also presented.

In this work we consider a left–right model containing mirror fermions with gauge group SU(3)_C ⊗ SU(2)_L ⊗ SU(2)_R ⊗ U(1)_Y′. The model has several free parameters which here we have calculated by using the recent values for the squared-neutrino mass differences. Lower bound for the mirror vacuum expectation value helped us to obtain crude estimations for some of these parameters. Also we estimate the order of magnitude of the masses of the standard and mirror neutrinos and numerical values for neutrino mixing angles.

We study the junction conditions for a nonspherical collapsing radiating star consisting of a shearing fluid undergoing radial heat flow with outgoing radiation. Radiation of the system is described by the plane symmetric version of the Vaidya solution. Junction conditions which match the collapse solutions to an exterior Vaidya metric show that, at the boundary, the pressure is proportional to the magnitude of the heat flow vector. Physical quantities, analogous to spherical symmetry related to the local conservation of momentum and surface redshift, are also obtained. Finally, exact gravitational collapse solutions, for both shear and shear-free cases, have been obtained by integrating a field equation.

We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space by means of an SU(1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng². In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of as a trivial bundle over the upper portion of the pseudosphere which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto using a global section of the solution on . Then we discuss the integration of the field equation using the Archimedes map . We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on .