Formation of Dark Matter Haloes in a Homogeneous Dark Energy Universe

Several independent cosmological tests have shown evidences that the energy density of the Universe is dominated by a dark energy component, which cause the present accelerated expansion. The large scale structure formation can be used to probe dark energy models, and the mass function of dark matter haloes is one of the best statistical tools to perform this study. We present here a statistical analysis of mass functions of galaxies under a homogeneous dark energy model, proposed in the work of Percival (2005), using an observational flux-limited X-ray cluster survey, and CMB data from WMAP. We compare, in our analysis, the standard Press-Schechter (PS) approach (where a Gaussian distribution is used to describe the primordial density fluctuation field of the mass function), and the PL (Power Law) mass function (where we apply a nonextensive q-statistical distribution to the primordial density field). We conclude that the PS mass function cannot explain at the same time the X-ray and the CMB data (even at 99% confidence level), and the PS best fit dark energy equation of state parameter is $\omega=-0.58$, which is distant from the cosmological constant case. The PL mass function provides better fits to the HIFLUGCS X-ray galaxy data and the CMB data; we also note that the $\omega$ parameter is very sensible to modifications in the PL free parameter, $q$, suggesting that the PL mass function could be a powerful tool to constrain dark energy models.Comment: 4 pages, 2 figures, Latex. Accepted for publication in the International Journal of Modern Physics D (IJMPD)

Black Hole Formation with an Interacting Vacuum Energy Density

We discuss the gravitational collapse of a spherically symmetric massive core of a star in which the fluid component is interacting with a growing vacuum energy density. The influence of the variable vacuum in the collapsing core is quantified by a phenomenological \beta-parameter as predicted by dimensional arguments and the renormalization group approach. For all reasonable values of this free parameter, we find that the vacuum energy density increases the collapsing time but it cannot prevent the formation of a singular point. However, the nature of the singularity depends on the values of \beta. In the radiation case, a trapped surface is formed for \beta<1/2 whereas for \beta>1/2, a naked singularity is developed. In general, the critical value is \beta=1-2/3(1+\omega), where the \omega-parameter describes the equation of state of the fluid component.Comment: 9 pages, 8 figure

Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid

By shifting the reference system for the local-density approximation (LDA) from the electron gas to other model systems one obtains a new class of density functionals, which by design account for the correlations present in the chosen reference system. This strategy is illustrated by constructing an explicit LDA for the one-dimensional Hubbard model. While the traditional {\it ab initio} LDA is based on a Fermi liquid (the electron gas), this one is based on a Luttinger liquid. First applications to inhomogeneous Hubbard models, including one containing a localized impurity, are reported.Comment: 4 pages, 4 figures (final version, contains additional applications and discussion; accepted by Phys. Rev. Lett.

Majority-Vote Model on a Random Lattice

The stationary critical properties of the isotropic majority vote model on random lattices with quenched connectivity disorder are calculated by using Monte Carlo simulations and finite size analysis. The critical exponents $\gamma$ and $\beta$ are found to be different from those of the Ising and majority vote on the square lattice model and the critical noise parameter is found to be $q_{c}=0.117\pm0.005$.Comment: 4 pages, 6 figure

Analysing and controlling the tax evasion dynamics via majority-vote model

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erd\"os-R\'enyi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhod of the noise critical $q_{c}$. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust and can be reproduced also through the nonequilibrium MVM on various topologies.Comment: 18 pages, 7 figures, LAWNP'09, 200

Cosmological particle production, causal thermodynamics, and inflationary expansion

Combining the equivalence between cosmological particle creation and an effective viscous fluid pressure with the fact that the latter represents a dynamical degree of freedom within the second-order Israel-Stewart theory for imperfect fluids, we reconsider the possibility of accelerated expansion in fluid cosmology. We find an inherent self-limitation for the magnitude of an effective bulk pressure which is due to adiabatic (isentropic) particle production. For a production rate which depends quadratically on the Hubble rate we confirm the existence of solutions which describe a smooth transition from inflationary to noninflationary behavior and discuss their interpretation within the model of a decaying vacuum energy density. An alternative formulation of the effective imperfect fluid dynamics in terms of a minimally coupled scalar field is given. The corresponding potential is discussed and an entropy equivalent for the scalar field is found.Comment: 16 pages, revtex file, submitted to Phys. Rev.

Non-nequilibrium model on Apollonian networks

We investigate the Majority-Vote Model with two states ($-1,+1$) and a noise $q$ on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter $q$. We also studies de effect of redirecting a fraction $p$ of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio $\gamma/\nu$, $\beta/\nu$, and $1/\nu$ for several values of rewiring probability $p$. The critical noise was determined $q_{c}$ and $U^{*}$ also was calculated. The effective dimensionality of the system was observed to be independent on $p$, and the value $D_{eff} \approx1.0$ is observed for these networks. Previous results on the Ising model in Apollonian Networks have reported no presence of a phase transition. Therefore, the results present here demonstrate that the Majority-Vote Model belongs to a different universality class as the equilibrium Ising Model on Apollonian Network.Comment: 5 pages, 5 figure

Inhomogeneous models of interacting dark matter and dark energy

We derive and analyze a class of spherically symmetric cosmological models whose source is an interactive mixture of inhomogeneous cold dark matter (DM) and a generic homogeneous dark energy (DE) fluid. If the DE fluid corresponds to a quintessense scalar field, the interaction term can be associated with a well motivated non--minimal coupling to the DM component. By constructing a suitable volume average of the DM component we obtain a Friedman evolution equation relating this average density with an average Hubble scalar, with the DE component playing the role of a repulsive and time-dependent $\Lambda$ term. Once we select an ``equation of state'' linking the energy density ($\mu$) and pressure ($p$) of the DE fluid, as well as a free function governing the radial dependence, the models become fully determinate and can be applied to known specific DE sources, such as quintessense scalar fields or tachyonic fluids. Considering the simple equation of state $p= (\gamma-1) \mu$ with $0\leq\gamma <2/3$, we show that the free parameters and boundary conditions can be selected for an adequate description of a local DM overdensity evolving in a suitable cosmic background that accurately fits current observational data. While a DE dominated scenario emerges in the asymptotic future, with total $\Omega$ and $q$ tending respectively to 1 and -1/2 for all cosmic observers, the effects of inhomogeneity and anisotropy yield different local behavior and evolution rates for these parameters in the local overdense region. We suggest that the models presented can be directly applied to explore the effects of various DE formalisms on local DM cosmological inhomogeneities.Comment: 15 pages, revtex4, 10 eps figure