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 ($\dot{H}> 0$)

Black hole collapse simulated by vacuum fluctuations with a moving semi-transparent mirror

Creation of scalar massless particles in two-dimensional Minkowski space-time--as predicted by the dynamical Casimir effect--is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a trajectory that simulates a black hole collapse (defined by Walker, and Carlitz and Willey), and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [r(w)=-i\alpha/(\w+i\alpha) and s(w)=\w/(\w+i\alpha), with $\alpha\geq 0$], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when $\alpha$ is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with results previously obtained in the literature. However, when $\alpha$ is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. We also show here that the reverse change of statistics takes place in a bidimensional fermionic model for massless particles, namely that the Fermi-Dirac statistics for the completely reflecting situation will turn into the Bose-Einstein statistics for a partially reflecting, physical mirror.Comment: 13 pages, no figures, version to appear in Physical Review

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

Qualitative study in Loop Quantum Cosmology

This work contains a detailed qualitative analysis, in General Relativity and in Loop Quantum Cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics the dynamics of a perfect fluid with a linear Equation of State (EoS). Dealing with the orbits (solutions) of the system, we will see that there are analytic ones, which lead to the same dynamics as the perfect fluid, and our goal is to check their stability, depending on the value of the EoS parameter, i.e., to show whether the other orbits converge or diverge to these analytic solutions at early and late times.Comment: 12 pages, 7 figures. Version accepted for publication in CQ

Possible polarisation and spin dependent aspects of quantum gravity

We argue that quantum gravity theories that carry a Lie algebraic modification of the Poincare' and Heisenberg algebras inevitably provide inhomogeneities that may serve as seeds for cosmological structure formation. Furthermore, in this class of theories one must expect a strong polarisation and spin dependence of various quantum-gravity effects.Comment: Awarded an "honourable mention" in the 2007 Gravity Research Foundation Essay Competitio

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

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.

Brane cosmology from observational surveys and its comparison with standard FRW cosmology

Several dark energy models on the brane are investigated. They are compared with corresponding theories in the frame of 4d Friedmann-Robertson-Walker cosmology. To constrain the parameters of the models considered, recent observational data, including SNIa apparent magnitude measurements, baryon acoustic oscillation results, Hubble parameter evolution data and matter density perturbations are used. Explicit formulas of the so-called {\it state-finder} parameters in teleparallel theories are obtained that could be useful to test these models and to establish a link between Loop Quantum Cosmology and Brane Cosmology. It is concluded that a joint analysis as the one developed here allows to estimate, in a very convenient way, possible deviation of the real universe cosmology from the standard Friedmann-Robertson-Walker one.Comment: 19 pages, 6 figures. arXiv admin note: text overlap with arXiv:1206.219

Bounce Loop Quantum Cosmology Corrected Gauss-Bonnet Gravity

We develop a Gauss-Bonnet extension of Loop Quantum Cosmology, by introducing holonomy corrections in modified $F(\mathcal{G})$ theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of Loop Quantum Gravity theories, and we result in having leading order corrections to the classical $F(\mathcal{G})$ theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes possible to find the Loop Quantum Cosmology corrected $F(\mathcal{G})$ theory that can realize various cosmological scenarios. Specifically, we studied exponential and power-law bouncing cosmologies, emphasizing on the behavior near the bouncing point and in some cases, the behavior for all the values of the cosmic time is obtained. We exemplify our theoretical constructions by using bouncing cosmologies, and we investigate which Loop Quantum Cosmology corrected Gauss-Bonnet modified gravities can successfully realize such cosmologies.Comment: Revised version, to appear in PR