Noncommutative quantum cosmology

We consider noncommutative quantum cosmology in the case of the low-energy string effective theory. Exact solutions are found and compared with the commutative case.     

Noncommutative quantum cosmology

We propose a model for noncommutative quantum cosmology by means of a deformation of minisuperspace. For the Kantowski-Sachs metric we are able to find the exact wave function. We construct wave packets and show that new quantum states that "compete" to be the most probable state appear, in clear contrast with the commutative case. A tunneling process could be possible among these states.     

Nonlinear quantum cosmology

We study the effects of an information-theoretically motivated nonlinear correction to the Wheeler-deWitt equation in the minisuperspace scheme for flat, k = 0, Friedmann–Robertson–Walker universes. When the only matter is a cosmological constant, the nonlinearity can provide a barrier that screens the original Big Bang, leading to the quantum creation of a universe through tunneling just as in the k = 1 case. When the matter is instead a free massless scalar field, the nonlinearity can again prevent a contracting classical universe from reaching zero size by creating a bounce. Our studies here are self-consistent to leading order in perturbation theory for the nonlinear effects.     

Canonical formulation of pp-waves

We construct a Hamiltonian formulation for the class of plane-fronted gravitational waves with parallel rays (pp-waves). Because of the existence of a light-like Killing vector, the dynamics is effectively reduced to a 2+1 evolution with “time” chosen to be light-like. In spite of the vanishing action this allows us to geometrically identify a symplectic form as well as dynamical Hamiltonian, thus casting the system into canonical form.     

Loop quantum cosmology: Recent progress

Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is sensitive to the quantum regime. As a consequence, the structure of and the approach to classical singularities are very different from general relativity. The quantum theory is free of singularities, and there are new phenomenological scenarios for the evolution of the very early universe such as inflation. We give an overview of the main effects, focussing on recent results obtained by different groups.     

Loop quantum cosmology: an overview

A brief overview of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the remarkable intuition that John Wheeler had. Discussion is organized at two levels. The the main text provides a bird’s eye view of the subject that should be accessible to non-experts. Appendices address conceptual and technical issues that are often raised by experts in loop quantum gravity and string theory.     

Canonical formulation of relativistic hydrodynamics

Canonical formulation of the relativistic theory of perfect fluids is given. As an introduction to this subject the canonical formalism for charged particles interacting with electromagnetic field is briefly discussed. Relativistic hydrodynamics is studied in several versions including hydrodynamics of charged fluids coupled to the electromagnetic field and ultrarelativistic hydrodynamics. Ultrarelativistic hydrodynamics is shown to be conformally invariant and several implications of conformal symmetry are discussed.