Marius J. Fullana

On the microwave background anisotropies produced by nonlinear voids

The Tolman-Bondi solution of the Einstein equations is used to study the microwave background anisotropy produced by a pressureless spherical cosmological inhomogeneity. Our method improves on previous ones because it does not involve any approximating condition and it allows us to assume the following: (1) a general Friedmann-Robertson-Walker background, (2) an arbitrary relative location of the observer and the inhomogeneity, (3) either an overdense or an underdense inhomogeneity with arbitrary size, (4) an arbitrary initial energy density profile, and (5) an arbitrary amplitude of the density contrast

On the Rees-Sciama effect: maps and statistics

Small maps of the Rees–Sciama (RS) effect are simulated by using an appropriate N-body code and a certain ray-tracing procedure. A method designed for the statistical analysis of cosmic microwave background (CMB) maps is applied to study the resulting simulations. These techniques, recently proposed – by our team – to consider lens deformations of the CMB, are adapted to deal with the RS effect. This effect and the deviations from Gaussianity associated to it seem to be too small to be detected in the near future. This conclusion follows from our estimation of both the RS angular power spectrum and the RS reduced n-direction correlation functions for n≤ 6.

Some invariants of discrete-time descriptor systems

Many papers analyze the role of controllability and observability indices of normal linear systems in control theory and their use in the study of structural properties. This work introduces these indices for linear discrete-time descriptor systems. Such indices are studied in two different ways, by means of the state-space approach and using its transfer matrix . A canonical form of the state-space system and a special decomposition of the nonproper transfer matrix are considered in order to discuss the reachability and observability indices.

On the horizons in a viable vector-tensor theory of gravitation

A certain vector-tensor (VT) theory of gravitation was tested in previous papers. In the background universe, the vector field of the theory has a certain energy density, which is appropriate to play the role of vacuum energy (cosmological constant). Moreover, this background and its perturbations may explain the temperature angular power spectrum of the cosmic microwave background (CMB) obtained with WMAP (Wilkinson Map Anisotropy Probe), and other observations, as e.g., the Ia supernova luminosities. The parametrized post-Newtonian limit of the VT theory has been proved to be identical to that of general relativity (GR), and there are no quantum ghosts and classical instabilities. Here, the stationary spherically symmetric solution, in the absence of any matter content, is derived and studied. The metric of this solution is formally identical to that of the Reissner-Nordström-de Sitter solution of GR, but the role of the electrical charge is played by a certain quantity Γ depending on both the vector field and the parameters of the VT theory. The black hole and cosmological horizons are discussed. The radius of the VT black hole horizon deviates with respect to that of the Kottler-Schwarzschild-de Sitter radius. Realistic relative deviations depend on Γ and reach maximum values close to 30 per cent. For large enough Γ values, there is no any black hole horizon, but only a cosmological horizon. The radius of this last horizon is almost independent of the mass source, the vector field components, and the VT parameters. It essentially depends on the cosmological constant value, which has been fixed by using cosmological observational data (CMB anisotropy, galaxy correlations and so on).