Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance

In canonical quantization of gravity, the state functional does not seem to depend on time. This hampers the physical interpretation of quantum gravity. I critically examine ten major attempts to circumvent this problem and discuss their shortcomings.

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Time and interpretations of quantum gravity

Aspects of superstring cosmology are reviewed with an emphasis on the cosmological implications of duality symmetries in the theory The string effective actions are summarized and toroidal compactification to four dimensions reviewed Global symmetries that arise in the compactification are discussed and the duality relationships between the string effective actions are then highlighted Higher-dimensional Kasner cosmologies are presented and interpreted in both string and Einstein frames, and then given in dimensionally reduced forms String cosmologies containing both non-trivial Neveu-Schwarz/Neveu-Schwarz and Ramond-Ramond fields are derived by employing the global symmetries of the effective actions Anisotropic and inhomogeneous cosmologies in four-dimensions are also developed The review concludes with a detailed analysis of the pre-big bang inflationary scenario The generation of primordial spectra of cosmological perturbations in such a scenario is discussed Possible future directions offered in the Horava-Witten theory are outlined

Superstring Cosmology

General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected We review the main mathematical properties of multi--connected spaces, and the different tools to classify them and to analyse their properties Following the mathematical classification, we describe the different possible muticonnected spaces which may be used to construct universe models We briefly discuss some implications of multi--connectedness for quantum cosmology, and its consequences concerning quantum field theory in the early universe We consider in details the properties of the cosmological models where space is multi--connected, with emphasis towards observable effects We then review the analyses of observational results obtained in this context, to search for a possible signature of multi--connectedness, or to constrain the models They may concern the distribution of images of cosmic objects like galaxies, clusters, quasars,, or more global effects, mainly those concerning the Cosmic Microwave Background, and the present limits resulting from them

Cosmic Topology

Relativistic Cosmology: The standard model and extensions

Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: Topologies and boundary conditions☆

Einstein’s vacuum field equations are solved for spacetimes with two−parameter spacelike symmetry, a space−reflection symmetry, and space sections homeomorphic to either S1×S2 or S3. All integrals are evaluated, and the spacetime metrics are presented in analytic form.

Closed gravitational−wave universes: Analytic solutions with two−parameter symmetry

The generalized projection‐tensor geometry introduced in an earlier article is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous article and obtain fully projected decompositions of Lie derivatives of the projection‐tensor field, the metric, and the projected parts of the metric. These results are applied to the analysis of space–times with isometries. The familiar cases of space–times with isotropic group orbits—cosmological models and spherical symmetry—are discussed as illustrations of the results.

Affine projection‐tensor geometry: Lie derivatives and isometries

The most efficient way to operate a rocket is to increase its exhaust velocity as it accelerates. When this increase is done properly, the final kinetic energy of the rocket is maximized. It is shown that the resulting ‘‘perfect rocket’’ is far simpler to analyze than the traditional constant‐thrust rocket and provides an excellent application of the material taught in all first semester noncalculus physics courses.

The physics of perfect rockets

Instantaneous Cauchy surfaces are defined and several of their properties are given. Instantaneous Cauchy surfaces are achronal surfaces whose Cauchy development interiors are maximal on the set of all achronal surfaces. It is shown that topology changes in such surfaces always result in nonempty future Cauchy horizons and departures from global hyperbolicity. It is also shown that the structure which is usually assumed for the background spacetime of a self‐consistent exploding black hole implies a topology change in instantaneous Cauchy surfaces.

Robert H. Gowdy

Papers

Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: Topologies and boundary conditions☆

Closed gravitational−wave universes: Analytic solutions with two−parameter symmetry

Affine projection‐tensor geometry: Lie derivatives and isometries

The physics of perfect rockets

Instantaneous Cauchy surfaces, topology change, and exploding black holes