Midisuperspace-Induced Corrections to the Wheeler De Witt Equation

We consider the midisuperspace of four dimensional spherically symmetric metrics and the Kantowski-Sachs minisuperspace contained in it. We discuss the quantization of the midisuperspace using the fact that the dimensionally reduced Einstein Hilbert action becomes a scalar-tensor theory of gravity in two dimensions. We show that the covariant regularization procedure in the midisuperspace induces modifications into the minisuperspace Wheeler DeWitt equation.Comment: 7 page

Topology Change in Canonical Quantum Cosmology

We develop the canonical quantization of a midisuperspace model which contains, as a subspace, a minisuperspace constituted of a Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar and dust fields, where the sign of the intrinsic curvature of the spacelike hypersurfaces of homogeneity is not specified, allowing the study of topology change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the midisuperspace model restricted to this minisuperspace subspace in the semi-classical approximation. Adopting the conditional probability interpretation, we find that some of the solutions present change of topology of the homogeneous hypersurfaces. However, this result depends crucially on the interpretation we adopt: using the usual probabilistic interpretation, we find selection rules which forbid some of these topology changes.Comment: 23 pages, LaTex file. We added in the conclusion some comments about path integral formalism and corrected litle misprinting

Gowdy T3T^3 Cosmological Models in N=1 Supergravity

We investigate the canonical quantization of supergravity N=1 in the case of a midisuperspace described by Gowdy $T^3$ cosmological models. The quantum constraints are analyzed and the wave function of the universe is derived explicitly. Unlike the minisuperspace case, we show the existence of physical states in midisuperspace models. The analysis of the wave function of the universe leads to the conclusion that the classical curvature singularity present in the evolution of Gowdy models is removed at the quantum level due to the presence of the Rarita-Schwinger field.Comment: 25 pages and 2 figure

Quantization of Midisuperspace Models

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit

Plane waves in quantum gravity: breakdown of the classical spacetime

Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees of freedom can be interpreted as an infinite and continuous set of annihilation and creation like variables. We also consider a simplified version of the model, in which the number of modes is restricted to a discrete set. In both cases, the quantization is achieved by introducing a Fock representation. We find regularized operators to represent the metric and discuss whether the coherent states of the quantum theory are peaked around classical spacetimes. It is shown that, although the expectation value of the metric on Killing orbits coincides with a classical solution, its relative fluctuations become significant when one approaches a region where null geodesics are focused. In that region, the spacetimes described by coherent states fail to admit an approximate classical description. This result applies as well to the vacuum of the theory.Comment: 11 pages, no figures, version accepted for publication in Phys. Rev.

Midisuperspace quantization: possibilities for fractional and emergent spacetime dimensions

Recently, motivated by certain loop quantum gravity inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second derivative theories of gravity exist (as revealed by the presence of three arbitrary functions in the corresponding Lagrangian/Hamiltonian) and not just those allowed by spherically symmetric general relativity. This freedom can be interpreted as the freedom to accommodate certain quantum gravity corrections in these models even in the absence of higher curvature terms (at a semi-classical level, at least). For a particular choice of the arbitrary functions it is shown that the new theories map to spherically symmetric general relativity in arbitrary number of (integer) dimensions thus explicitly demonstrating that when working with midisuperspace models, one loses the information about the dimensionality of the full spacetime. In addition, it is shown that these new theories can accommodate scenarios of fractional spacetime dimensions as well as those of emergent spacetime dimensions -- a possibility suggested by various approaches to quantum gravity.Comment: 10 page