A Brief Introduction to Loop Quantum Cosmology

In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of holonomies and fluxes. In order to discuss its physical implications, a lot of attention has been paid to the application of the quantization techniques of Loop Quantum Gravity to symmetry reduced models with cosmological solutions, a line of research that has been called Loop Quantum Cosmology. We summarize its fundamentals and the main differences with respect to the more conventional quantization approaches employed in cosmology until now. In addition, we comment on the most important results that have been obtained in Loop Quantum Cosmology by analyzing simple homogeneous and isotropic models. These results include the resolution of the classical big-bang singularity, which is replaced by a quantum bounce.Comment: 15 pages, published in AIP Conference Proceedings, Volume 1130, Geometry and Physics: XVII International Fall Workshop on Geometry and Physic

Involutions on the Algebra of Physical Observables From Reality Conditions

Some aspects of the algebraic quantization programme proposed by Ashtekar are revisited in this article. It is proved that, for systems with first-class constraints, the involution introduced on the algebra of quantum operators via reality conditions can never be projected unambiguously to the algebra of physical observables, ie, of quantum observables modulo constraints. It is nevertheless shown that, under sufficiently general assumptions, one can still induce an involution on the algebra of physical observables from reality conditions, though the involution obtained depends on the choice of particular representatives for the equivalence classes of quantum observables and this implies an additional ambiguity in the quantization procedure suggested by Ashtekar.Comment: 19 pages, latex, no figure

Interest Rate Rules, Inflation Stabilization, and Imperfect Credibility: The Small Open Economy Case

The paper examines the robustness of Interest Rate Rules, IRRs, in the context of an imperfectly credible stabilization program, closely following the format of much of the literature in open-economy models, e.g., Calvo and Végh (1993 and 1999). A basic result is that IRRs, like Exchange Rate Based Stabilization, ERBS, programs, could give rise to macroeconomic distortion, e.g., underutilization of capacity and real exchange rate misalignment. However, while under imperfect credibility EBRS is associated with overheating and current account deficits, IRRs give rise to somewhat opposite results. Moreover, the paper shows that popular policies to counteract misalignment, like Strategic Foreign Exchange Market Intervention or Controls on International Capital Mobility may not be effective or could even become counterproductive. The bottom line is that the greater exchange rate flexibility granted by IRRs is by far not a sure shot against the macroeconomic costs infringed by imperfect credibility.