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This work analyzes the effects of quantization on a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) model with positive curvature and material content composed of a Bose-Einstein condensate, a radioactive fluid and a cosmological constant playing the role of the dark energy of the universe. The quantization of the model was performed using the finite difference method in the Crank-Nicolson scheme: solutions of the Wheeler-DeWitt equation are obtained, in the form of finite norm wave packets which are well defined in all space, even if the 3D-sphere is degenerate. The introduction of the Bose-Einstein condensate and cosmological constant preserves the existence of bounce solutions (for certain choices of parameters and initial conditions) with exits for inflation (de Sitter solutions). This occurs after the universe emerges from its quantum phase by a tunneling mechanism., Comment: 30 pages, 15 figures, 3 tables The authors are fully reviewing this article

In this work we propose the quantization of a cosmological model describing the primordial universe filled with five barotropic fluids, namely: radiation, dust, vacuum, cosmic strings and domain walls. We intend to identify which fluid is best suited to provide phenomenologically the temporal variable in accordance with the observable universe. Through the Galerkin spectral method and the finite difference method in the Crank-Nicolson scheme (vacuum case), the quantum cosmological solutions are obtained and compared. We, also, compare the quantum cosmological solutions with the corresponding classical ones. The vacuum case is especially interesting because it provides a tunneling transition mechanism from the quantum to the classical phase and the possibility of calculating quantum tunneling probabilities., Comment: 26 pages, 25 figures, 2 tables

The dynamics of adoption of innovations is an important subject in many fields and areas, like technological development, industrial processes, social behavior, fashion or marketing. The number of adopters of a new technology generally increases following a kind of logistic function. However, empirical data provide evidences that this behavior may be more complex, as many factors influence the decision to adopt an innovation. On the one hand, although some individuals are inclined to adopt an innovation if many people do the same, there are others who act in the opposite direction, trying to differentiate from the "herd". People who prefer to behave like the others are called mimetic, whereas individuals who resist adopting new products, the stronger the greater the number of adopters, are named contrarians. On the other hand, new adopters may have second thoughts and change their decisions accordingly. Agents who regret and abandon their decision will be denominated repentant. In this paper we investigate a simple model for the adoption of an innovation for a society composed by mimetic and contrarian individuals whose decisions depend mainly on three elements: the appeal of the novelty, the inertia or resistance to adopt it, and the social interactions with other agents. In the process, agents can repent and turn back to the old technology. We present analytic calculations and numerical simulations to determine the conditions for the establishment of the new technology. The inclusion of repentant agents modify the balance between the global incentive to adopt and the number of contrarians who prevent full adoption, generating a rich landscape of temporal evolution that includes cycles of adoption.

In this work we derive a scenario {in which} the early universe consists of {radiation fluid} and Bose-Einstein condensate. The possibility of gravitational self-interaction due to an attractive Bose-Einstein condensate is analyzed. The classical behavior of the scale factor of the universe is determined by a parameter associated with the Bose-Einstein fluid with bouncing or Big Crunch solutions. After we proceed to compute the finite-norm wave packet solutions to the Wheeler-DeWitt equation. The behavior of the scale factor is studied by applying the many-worlds interpretation of quantum mechanics. The quantum cosmological model is free from the singularities., Comment: 8 figures, 1 Table, 18 pages

We review the Eulerian description of hidrodynamics using Seliger-Whitham's formalism (in classical case) and Schutz's formalism (in relativistic case). In these formalisms, the velocity field of a perfect fluid is described by scalar potentials. With this we can obtain the evolution equations of the fluid and its Hamiltonian. In the scenario of quantum cosmology the Schutz's formalism makes it possible to introduce phenomenologically a time variable in minisuperspace models., Comment: 26 pages, accepted for publication in Brazilian Journal of Physics, in press

In this work the homogeneous and isotropic Universe of Friedmann-Robertson-Walker is studied in the presence of two fluids: stiff matter and radiation described by the Schutz's formalism. We obtain to the classic case the behaviour of the scale factor of the universe. For the quantum case the wave packets are constructed and the wave function of the universe is found., Comment: 17 pages and 21 figures

In this paper we study the quantum cosmological Kantowski-Sachs model and solve the Wheeler-DeWitt equation in minisuperspace to obtain the wave function of the corresponding universe. The perfect fluid is described by the Schutz's canonical formalism, which allows to attribute dynamical degrees of freedom to matter. The time is introduced phenomenologically using the fluid's degrees of freedom. In particular, we adopt a stiff matter fluid. The viability of this model is analyzed and discussed., Comment: 12 pages

We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state $p = \alpha\rho + k\rho^{1 + 1/n}$. We calculate the dynamics of the scalar factor and build a Universe with constant density at the origin. We also find the equivalent scalar field that could create such equation of state and calculate the corresponding slow-roll parameters. We calculate the scalar perturbations, the scalar power spectrum and the spectral index., Comment: 16 pages, 4 figures

In the present work, we analyze the evolution of the scalar and tensorial perturbations and the quantities relevant for the physical description of the Universe, as the density contrast of the scalar perturbations and the gravitational waves energy density during the Bose-Einstein condensation of dark matter. The behavior of these parameters during the Bose-Einstein phase transition of dark matter is analyzed in details. To study the cosmological dynamics and evolution of scalar and tensorial perturbations in a Universe with and without cosmological constant we use both analytical and numerical methods. The Bose-Einstein phase transition modifies the evolution of gravitational waves of cosmological origin, as well as the process of large-scale structure formation., Comment: 22 pages, 8 figures, accepted for publication in JCAP

We discuss how different cosmological models of the Universe affect the probability that a background source has multiple images related by an angular distance $\theta_E$ of the line of sight, \textit{i. e.}, the optical depth of gravitational lensing. We examine some cosmological models for different values of the density parameter $\Omega_i$: i) the cold dark matter model, ii) the $\Lambda$CDM model, iii) the Bose-Einstein condensate dark matter model, iv) the Chaplygin gas model, v) the viscous fluid cosmological model and vi) the holographic dark energy model. We note that the dependence of the energy-matter content of the universe profoundly alters the frequency of multiple quasar image., Comment: 23 pages, 10 figures, accepted for publication in Astrophysics and Space Science

We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every time it interacts with another agent who has a different opinion. The dynamics leads to size distributions of clusters (made up of agents which have the same opinion and are located at contiguous spatial positions) which follow a power law, as long as the range of the interaction between the agents is not too short, i.e. the system self-organizes into a critical state. Short range interactions lead to an exponential cut off in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped. When the diversity of opinions is restricted to two, non-consensus dynamic is observed, with unequal population fractions, whereas consensus is reached if the agents are also allowed to interact with those which are located far from them.

We investigate the quantum origin of the primordial cosmological gravitational waves in the Brans-Dicke theory in the two conformally related frames, the Jordan-Brans-Dicke frame and the Einstein frame. We calculated the theoretical observable in both frames and we compared both with General Relativity. We compute the number of gravitons $N_k$ produced during inflation and the observables: power spectrum $P_T$, spectral index $n_T$ and energy density $\Omega_k$. The comparison shows that for the case of the particles number $N_k$ the results are the same in both frames and in General Relativity when the Brans-Dicke parameter is much bigger than unity. For the spectral index $n_T$ we show that it is possible to get a scale invariant perturbation in the Jordan-Brans-Dicke frame when $\omega\rightarrow\infty$ and in the Einstein frame when $\omega\rightarrow\pm\infty$. In both frames, the results found for the power spectrum $P_T$ and the energy density $\Omega$ show that the prefered values of $\omega$ are diferente from that that are found in the local tests., Comment: 23 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1102.0995

We investigate the quantum origin of the primordial cosmological gravitational waves in the Brans-Dicke theory. We compute the number of gravitons $N_k$ produced during inflation and the observables: power spectrum $P_T$, spectral index $n_T$ and energy density $\Omega_k$. By comparison with General Relativity we see that the results for both theories are the same for the case of the particles number $N_k$ and for the case of the power spectrum $P_T$ and the energy density $\Omega$ only when $\omega<10$. For the spectral index $n_T$ we found that when the Brans-Dicke coupling parameter $\omega$ is bigger than unity the spectral index approximates the expression found in the General Relativity. This may awake us to the possibility that $\omega$ varies with the cosmological scale., Comment: 19 pages, 9 figures

We study the Generalized Chaplygin gas model (GCGM) using Gamma-ray bursts as cosmological probes. In order to avoid the so-called circularity problem we use cosmology-independent data set and Bayesian statistics to impose constraints on the model parameters. We observe that a negative value for the parameter $\alpha$ is favoured if we adopt a flat Universe and the estimated value of the parameter $H_{0}$ is lower than that found in literature., Comment: 10 pages, 29 figures, accepted for publication in Physics Letters B

The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that fixed time delays destabilize the steady state solution of the standard SIRS model, giving rise to stable oscillations for certain parameters values. In this contribution, starting from the classical SIRS model, we make a general treatment of the recovery and loss of immunity terms. We present oscillation diagrams (amplitude and period) in terms of the parameters of the model, showing how oscillations can be destabilized by the shape of the distributions of the two characteristic (infectious and immune) times. The formulation is made in terms of delay equation which are both numerical integrated and linearized. Results from simulation are included showing where they support the linear analysis and explaining why not where they do not. Considerations and comparison with real diseases are presented along., Comment: 18 pages, 12 figures

We model the cosmic medium as the mixture of a generalized Chaplygin gas and a pressureless matter component. Within a neo-Newtonian approach we compute the matter power spectrum. The 2dFGRS data are used to discriminate between unified models of the dark sector and different models, for which there is separate dark matter, in addition to that accounted for by the generalized Chaplygin gas. Leaving the corresponding density parameters free, we find that the unified models are strongly disfavored. On the other hand, using unified model priors, the observational data are also well described, in particular for small and large values of the generalized Chaplygin gas parameter $\alpha$., Comment: Latex file, 5 pages, 11 figures in eps format. For the proceedings of the conference Dark Energy and Dark Matter, 7-11 july 2008, Lyon, France

We model the cosmic medium as the mixture of a generalized Chaplygin gas and a pressureless matter component. Within a neo-Newtonian approach (in which, different from standard Newtonian cosmology, the pressure enters the homogeneous and isotropic background dynamics) we compute the matter power spectrum. The 2dFGRS data are used to discriminate between unified models of the dark sector (a purely baryonic matter component of roughly 5 percent of the total energy content and roughly 95 percent generalized Chaplygin gas) and different models, for which there is separate dark matter, in addition to that accounted for by the generalized Chaplygin gas. Leaving the corresponding density parameters free, we find that the unified models are strongly disfavored. On the other hand, using unified model priors, the observational data are also well described, in particular for small and large values of the generalized Chaplygin gas parameter $\alpha$. The latter result is in agreement with a recent, more qualitative but fully relativistic, perturbation analysis in Gorini et al., Comment: Latex file, 17 pages, 29 figures in eps format

Scalar perturbations can grow during a phantomic cosmological phase as the big rip is approached, in spite of the high accelerated expansion regime, if the equation of state is such that $\frac{p}{\rho} = \alpha < - {5/3}$. It is shown that such result is independent of the spatial curvature. The perturbed equations are exactly solved for any value of the curvature parameter $k$ and of the equation of state parameter $\alpha$. Growing modes are found asymptotically under the condition $\alpha < - {5/3}$. Since the Hubble radius decreases in a phantom universe, such result indicates that a phantom scenario may not survive longtime due to gravitational instability., Comment: Latex file, 6 pages

The modeling of the early universe is done through the quantization of a Friedmann-Robertson-Walker model with positive curvature. The material content consists of two fluids: radiation and Chaplygin gas. The quantization of these models is made by following the Wheeler and DeWitt's prescriptions. Using the Schutz formalism, the time notion is recovered and the Wheeler-DeWitt equation transforms into a time dependent Schr\"{o}dinger equation, which rules the dynamics of the early universe, under the action of an effective potential $V_{ef}$. Using a finite differences method and the Crank-Nicholson scheme, in a code implemented in the program OCTAVE, we solve the corresponding time dependent Schr\"{o}dinger equation and obtain the time evolution of a initial wave packet. This wave packet satisfies appropriate boundary conditions. The calculation of the tunneling probabilities shows that the universe may emerge from the Planck era to an inflationary phase. It also shows that, the tunneling probability is a function of the mean energy of the initial wave packet and of two parameters related to the Chaplygin gas. We also show a comparison between these results and those obtained by the WKB approximation., Comment: Revtex file with 12 pages and 6 PS figures