Conference

A classical Hamiltonian system can be reduced to a subsystem of "relevant observables" using the pull-back under a Poisson embedding of the "relevant phase space" into the "full phase space". Since a quantum theory can be thought of a noncommutative phase space, one encounters the problem of the embedding of noncommutative spaces, when one tries to extend the reduction via a pull-back to a quantum theory. This problem can be solved for a class of physically interesting quantum systems and embeddings using an analogy to finding the base space of an embedded fibre bundle via the projection in the full fibre bundle. The resulting construction is then applied to Loop Quantum Gravity to extract a cosmological sector. This sector turns out to be similar but not equivalent to Loop Quantum Cosmology.

The description of noncommutative space will be given. I will show the relation between field theory on kappa-Minkowski space and the one in Minkowski. This construction leads to deformed energy momentum conservation law for energies close to the Planck scale.

At large scales the CMB spectrum measured by WMAP appears to have an anomalously low power of the quadrupole and an asymmetry of power at l < 40. We show that with an initial stage of fast roll of the inflation and a gradient in the initial conditions a simple chaotic inflation model may be capable of explaining both anomalies.

I consider a six dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, I show that the gravitational interaction between sources on the brane is described by Einstein 4d gravity at large distances. This is one of the first complete study of gravity in a realistic brane model with two extra dimensions, in which the mechanism of stabilization of the extra space is fully taken into account.

I discuss two instances in which nonlinear perturbations in cosmological models are important. First, in de Sitter space-time, the bare necessity that the perturbations should be part of a consistent Taylor expansion of the field equations leads to the requirement, using the 'linearization stability' arguments of the '70's, that the quantum field theory of a scalar field on de Sitter space-time is manifestly de Sitter invariant (not covariant). Second, the concern that in slow-roll inflation the effect of second order perturbations on the long wavelength (super Hubble) perturbations could be much stronger than that of the first order perturbations, for a wide range of slow-roll conditions, is explored in the context of a linear inflation potential and chaotic inflation.