Phenomenological description of quantum gravity inspired modified classical electrodynamics

We discuss a large class of phenomenological models incorporating quantum gravity motivated corrections to electrodynamics. The framework is that of electrodynamics in a birefringent and dispersive medium with non-local constitutive relations, which are considered up to second order in the inverse of the energy characterizing the quantum gravity scale. The energy-momentum tensor, Green functions and frequency dependent refraction indices are obtained, leading to departures from standard physics. The effective character of the theory is also emphasized by introducing a frequency cutoff. The analysis of its effects upon the standard notion of causality is performed, showing that in the radiation regime the expected corrections get further suppressed by highly oscillating terms, thus forbiding causality violations to show up in the corresponding observational effects.Comment: 14 pages, to be published in Obregon Festschrift 2006, Gen. Rel. and Gra

Numerical loop quantum cosmology: an overview

A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key prediction of the bounce at the Planck scale in different models, and the numerical methods used to analyze the properties of the quantum difference operator and the von Neumann stability issues. Using the quantization of a massless scalar field in an isotropic spacetime as a template, an attempt is made to highlight the complementarity of different methods to gain understanding of the new physics emerging from the quantum theory. Open directions which need to be explored with more refined numerical methods are discussed.Comment: 33 Pages, 4 figures. Invited contribution to appear in Classical and Quantum Gravity special issue on Non-Astrophysical Numerical Relativit