Singularity avoidance by collapsing shells in quantum gravity

We discuss a model describing exactly a thin spherically symmetric shell of matter with zero rest mass. We derive the reduced formulation of this system in which the variables are embeddings, their conjugate momenta, and Dirac observables. A non-perturbative quantum theory of this model is then constructed, leading to a unitary dynamics. As a consequence of unitarity, the classical singularity is fully avoided in the quantum theory.Comment: 5 pages, 1 figure, received honorable mention in the 2001 essay competititon, to appear in Int. J. Mod. Phys.

Quantum Gravitational Contributions to the CMB Anisotropy Spectrum

We derive the primordial power spectrum of density fluctuations in the framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field. In this way we first recover the scale-invariant power spectrum that is found as an approximation in the simplest inflationary models. We then obtain quantum gravitational corrections to this spectrum and discuss whether they lead to measurable signatures in the CMB anisotropy spectrum. The non-observation so far of such corrections translates into an upper bound on the energy scale of inflation.Comment: 4 pages, v3: sign error in Eq. (5) and its consequences correcte

Remarks on the issue of time and complex numbers in canonical quantum gravity

We develop the idea that, as a result of the arbitrariness of the factor ordering in Wheeler-DeWitt equation, gauge phases can not, in general, being completely removed from the wave functional in quantum gravity. The latter may be conveniently described by means of a remnant complex term in WDW equation depending of the factor ordering. Taking this equation for granted we can obtain WKB complex solutions and, therefore, we should be able to derive a semiclassical time parameter for the Schroedinger equation corresponding to matter fields in a given classical curved space.Comment: Typewritten using RevTex, to appear in Phys. Rev.

Quantum Gravity Equation In Schroedinger Form In Minisuperspace Description

We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time that enters into the Schroedinger equation. Without any reference to the Wheeler-DeWitt equation and without invoking the expansion of exponent in WKB wavefunction in powers of Planck mass, we obtain an equation for quantum gravity in Schroedinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter field equation our equation is equivalent to the Wheeler-DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler-DeWitt equation provided one evaluates the normalization constant according to the wormhole dominance proposal recently proposed by us.Comment: 11 Pages, ReVTeX, no figur

Solving the Problem of Time in Mini-superspace: Measurement of Dirac Observables

One solution to the so-called problem of time is to construct certain Dirac observables, sometimes called evolving constants of motion. There has been some discussion in the literature about the interpretation of such observables, and in particular whether single Dirac observables can be measured. Here we clarify the situation by describing a class of interactions that can be said to implement measurements of such observables. Along the way, we describe a useful notion of perturbation theory for the rigging map eta of group averaging (sometimes loosely called the physical state "projector"), which maps states from the auxiliary Hilbert space to the physical Hilbert space.Comment: 12 pages, ReVTe

Emergent charge ordering in near half doped Na0.46_{0.46}CoO2_{2}

We have utilized neutron powder diffraction to probe the crystal structure of layered Na$_{x}$CoO$_{2}$ near the half doping composition of $x=$0.46 over the temperature range of 2 to 600K. Our measurements show evidence of a dynamic transition in the motion of Na-ions at 300K which coincides with the onset of a near zero thermal expansion in the in-plane lattice constants. The effect of the Na-ordering on the CoO$_{2}$ layer is reflected in the octahedral distortion of the two crystallographically inequivalent Co-sites and is evident even at high temperatures. We find evidence of a weak charge separation into stripes of Co$^{+3.5+\epsilon}$ and Co$^{+3.5-\epsilon}$, $\epsilon\sim0.06e$ below \Tco=150K. We argue that changes in the Na(1)-O bond lengths observed at the magnetic transition at \tm=88K reflect changes in the electronic state of the CoO$_{2}$ layerComment: 7 pages, 6 figures, in press Phys. Rev.

Semiclassical approximation to supersymmetric quantum gravity

We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schrodinger equation, and quantum gravitational correction terms to this Schrodinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many fingered) local time parameter has to be present on $SuperRiem \Sigma$ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early universe. The physical meaning of these equations and results, in particular the similarities to and differences from the pure bosonic case, are discussed.Comment: 34 pages, clarifications added, typos correcte

Time in Quantum Gravity

The Wheeler-DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting from Wheeler-DeWitt equation and WKB ansatz for the WD wavefunction. The approach has some drawbacks. In this work, we obtain the time-contained Schroedinger-Wheeler-DeWitt equation without using the WD equation and the WKB ansatz for the wavefunction. We further show that a Gaussian ansatz for SWD wavefunction is consistent with the Hartle-Hawking or wormhole dominance proposal boundary condition. We thus find an answer to the small scale boundary conditions.Comment: 12 Pages, LaTeX, no figur