Bouncing Loop Quantum Cosmology from F(T)F(T) gravity

The big bang singularity could be understood as a breakdown of Einstein's General Relativity at very high energies. Adopting this viewpoint, other theories, that implement Einstein Cosmology at high energies, might solve the problem of the primeval singularity. One of them is Loop Quantum Cosmology (LQC) with a small cosmological constant that models a universe moving along an ellipse, which prevents singularities like the big bang or the big rip, in the phase space $(H,\rho)$, where $H$ is the Hubble parameter and $\rho$ the energy density of the universe. Using LQC when one considers a model of universe filled by radiation and matter where, due to the cosmological constant, there are a de Sitter and an anti de Sitter solution. This means that one obtains a bouncing non-singular universe which is in the contracting phase at early times. After leaving this phase, i.e., after bouncing, it passes trough a radiation and matter dominated phase and finally at late times it expands in an accelerated way (current cosmic acceleration). This model does not suffer from the horizon and flatness problems as in big bang cosmology, where a period of inflation that increases the size of our universe in more than 60 e-folds is needed in order to solve both problems. The model has two mechanisms to avoid these problems: The evolution of the universe through a contracting phase and a period of super-inflation ($\dot{H}> 0$)

On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

In this paper we study the maximum number $N$ of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies $2\leq N \leq 3$ if one of the two linear differential systems has its equilibrium point on the straight line of discontinuity

The Transition. Convergence and discrepancy in the international and national press coverage of Spain’s major postwar international news export

The role of the national and foreign press in the news coverage of the Spanish transition to democracy (1975-1978) has been a constant reference in the historical study of the period of political change after the end of the Francoist dictatorship. In this article we present the general results of three research projects concerning the role of the foreign press, of the Spanish daily press and the magazine marketin which we can observe both convergence and discrepance in the news narrative, editorial behaviour and political standpoints. The greater independence and informative freedom of the foreign press contrasts with the proximity of the Spanish press to both King and government with the exception of the critical support to reform expressed in both the new political magazines and newspapers during the first few months of the process of political change.El papel de la prensa nacional y extranjera en la cobertura informativa de la Transición española a la democracia (1975-1978) ha sido una referencia constante en la historiografía del período de cambio político en España tras el final de la dictadura de Franco, así como en la cultura periodística. En este artículo presentamos los resultados generales de tres proyectos de investigación sobre el papel de la prensa extranjera, de la prensa diaria española y de la prensa no diaria enlos que se pueden comprobar convergencias y discrepancias en el relato informativo, las valoraciones editoriales y los posicionamientos políticos. La mayor independencia y libertad informativa de la prensa extranjera contrasta con la proximidad de la prensa española al rey y al gobierno, con la excepción del apoyo crítico a la reforma de las nuevas revistas políticas y los diarios surgidos en los primeros meses del proceso de cambio político

Viable Inflationary Evolution from Loop Quantum Cosmology Scalar-Tensor Theory

In this work we construct a bottom-up reconstruction technique for Loop Quantum Cosmology scalar-tensor theories, from the observational indices. Particularly, the reconstruction technique is based on fixing the functional form of the scalar-to-tensor ratio as a function of the $e$-foldings number. The aim of the technique is to realize viable inflationary scenarios, and the only assumption that must hold true in order for the reconstruction technique to work is that the dynamical evolution of the scalar field obeys the slow-roll conditions. We shall use two functional forms for the scalar-to-tensor ratio, one of which corresponds to a popular inflationary class of models, the $\alpha$-attractors. For the latter, we shall calculate the leading order behavior of the spectral index and we shall demonstrate that the resulting inflationary theory is viable and compatible with the latest Planck and BICEP2/Keck-Array data. In addition, we shall find the classical limit of the theory, and as we demonstrate, the Loop Quantum Cosmology corrected theory and the classical theory are identical at leading order in the perturbative expansion quantified by the parameter $\rho_c$, which is the critical density of the quantum theory. Finally, by using the formalism of slow-roll scalar-tensor Loop Quantum Cosmology, we shall investigate how several inflationary potentials can be realized by the quantum theory, and we shall calculate directly the slow-roll indices and the corresponding observational indices. In addition, the $f(R)$ gravity frame picture is presented.Comment: PRD Accepte

Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This fact has been used to conjecture that the resulting models correspond to the spatially homogeneous (SH) models of Bianchi type I, at least for the case where the cosmological constant vanish. By exploiting the full set of the constraint equations as expressed in the 1+3 covariant formalism and using elements from the theory of the spacelike congruences, we provide a direct and simple proof of this conjecture for vacuum and dust fluid models, which shows that the Szekeres family of solutions represents the most general class of SIIS models. The suggested procedure also shows that, the uniqueness of the SIIS of the Petrov type D is not, in general, affected by the presence of a non-zero pressure fluid. Therefore, in order to allow a broader class of Petrov type I solutions apart from the SH models of Bianchi type I, one should consider more general ``silent'' configurations by relaxing the vanishing of the vorticity and the magnetic part of the Weyl tensor but maintaining their ``silence'' properties i.e. the vanishing of the curls of $E_{ab},H_{ab}$ and the pressure $p$.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an appendix are added; (v3) minor changes to match published versio

Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has center, a real one for $y<0$ and a virtual one for $y>0$, and such that the real center is a global center. Then, working with a first order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation.Comment: 24 pages, 7 figure

Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the switching manifold is added to the second order averaged function

Hamiltonian approach to the dynamical Casimir effect

A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term --proportional to the mirrors' acceleration-- which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors --while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out.Comment: 4 pages, no figures; version published in Phys. Rev. Lett. 97 (2006) 13040

Bifurcations from families of periodic solutions in piecewise differential systems

Consider a differential system of the form $$x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon),$$ where $F_i:\mathbb{S}^1 \times D \to \mathbb{R}^m$ and $R:\mathbb{S}^1 \times D \times (-\varepsilon_0,\varepsilon_0) \to \mathbb{R}^m$ are piecewise $C^{k+1}$ functions and $T$-periodic in the variable $t$. Assuming that the unperturbed system $x'=F_0(t,x)$ has a $d$-dimensional submanifold of periodic solutions with $d<m$, we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated $T$-periodic solutions of the above differential system

Viscous Cosmology for Early- and Late-Time Universe

From a hydrodynamicist's point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (excluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy-Verlinde formula is affected by viscosity.Comment: 71 pages, Invited Review for Int.J.Mod.Phys.