Annual Report 2003 - Vatican Observatory

VATICAN OBSERVATORYI. Astronomical ResearchTheoretical Studies, Astrophysics, and CosmologyIn collaboration with the group of mathematicians of Warsaw Technical University,HELLER continued the program on applications of noncommutative geometry to physics.They have made substantial progress in constructing a model unifying general relativityand quantum mechanics. Since the model is based on a finite group, it was possibleto compute it in all its details, resulting in clarification of several problems encounteredin previous work.HELLER continues to research the status of time in relativistic cosmology and, in particular,in fundamental theories based on noncommutative geometry. In the latter theories,time is not given a priori but emerges out of the primordial atemporal (and aspacial)physics. He is also working on the problems, both technical and conceptual, connectedwith the Majid program to construct the fundamental physical theory based onthe theory of quantum groups.STOEGER and ARAÚJO (Universidade Federal do Rio de Janeiro) are nearing completionof their project of specifying and implementing a detailed procedure for solving theEinstein field equations in observational coordinates with cosmological data functionsfor general perturbations to Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologicalmodels. This includes both the case in which there is just dust (pressure-freematter) and the more difficult case in which there is both dust and vacuum energy (acosmological constant).STOEGER AND RIBEIRO (Physics Institute, Universidade Federal do Rio de Janeiro)are beginning to extend their completed work, relating galaxy luminosity functions torelativistic energy density and to number counts in the case of Einstein de Sitter cosmologies(flat universe models), to other FLRW cases, including those with a non-zerocosmological constant (vacuum energy). Once that is finished, they will be applyingtheir approach to Lemaître-Bondi-Tolman cosmological models (which are isotropic,but not spatially homogeneous) and to perturbed-FLRW models. They also are beginningto investigate how to include improved models of galaxy number and luminosityevolution in their procedure.Following up on earlier work he did with ELLIS, DUNSBY, and McEWAN(Department of Mathematics, University of Cape Town), STOEGER is continuing hisinvestigations of mixed radiation-vacuum energy epochs in the very early universe, justafter the Planck era and just before inflation. This study hopefully will shed further lighton the constraints that adequate inflation places on the relative amounts of radiation andvacuum energy at these early times and, therefore, on some of the conditions necessaryfor inflation itself. Connected with this work, STOEGER is also pursuing research on16