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

The Coherence of Primordial Fluctuations Produced During Inflation

The behaviour of quantum metric perturbations produced during inflation is considered at the stage after the second Hubble radius crossing. It is shown that the classical correlation between amplitude and momentum of a perturbation mode, previously shown to emerge in the course of an effective quantum-to-classical transition, is maintained for a sufficiently long time, and we present the explicit form in which it takes place using the Wigner function. We further show with a simple diffraction experiment that quantum interference, non-expressible in terms of a classical stochastic description of the perturbations, is essentially suppressed. Rescattering of the perturbations leads to a comparatively slow decay of this correlation and to a complete stochastization of the system.Comment: LaTeX (7 pages

Classical and quantum LTB model for the non-marginal case

We extend the classical and quantum treatment of the Lemaitre-Tolman-Bondi (LTB) model to the non-marginal case (defined by the fact that the shells of the dust cloud start with a non-vanishing velocity at infinity). We present the classical canonical formalism and address with particular care the boundary terms in the action. We give the general relation between dust time and Killing time. Employing a lattice regularization, we then derive and discuss for particular factor orderings exact solutions to all quantum constraints.Comment: 23 pages, no figures, typos correcte

Quantum cosmology with big-brake singularity

We investigate a cosmological model with a big-brake singularity in the future: while the first time derivative of the scale factor goes to zero, its second time derivative tends to minus infinity. Although we also discuss the classical version of the model in some detail, our main interest lies in its quantization. We formulate the Wheeler-DeWitt equation and derive solutions describing wave packets. We show that all such solutions vanish in the region of the classical singularity, a behaviour which we interpret as singularity avoidance. We then discuss the same situation in loop quantum cosmology. While this leads to a different factor ordering, the singularity is there avoided, too.Comment: 24 pages, 7 figures, figures improved, references added, conceptual clarifications include

Consistency of Semiclassical Gravity

We discuss some subtleties which arise in the semiclassical approximation to quantum gravity. We show that integrability conditions prevent the existence of Tomonaga-Schwinger time functions on the space of three-metrics but admit them on superspace. The concept of semiclassical time is carefully examined. We point out that central charges in the matter sector spoil the consistency of the semiclassical approximation unless the full quantum theory of gravity and matter is anomaly-free. We finally discuss consequences of these considerations for quantum field theory in flat spacetime, but with arbitrary foliations.Comment: 12 pages, LATEX, Report Freiburg THEP-94/2

On time and the quantum-to-classical transition in Jordan-Brans-Dicke quantum gravity

Any quantum theory of gravity which treats the gravitational constant as a dynamical variable has to address the issue of superpositions of states corresponding to different eigenvalues. We show how the unobservability of such superpositions can be explained through the interaction with other gravitational degrees of freedom (decoherence). The formal framework is canonically quantized Jordan-Brans-Dicke theory. We discuss the concepts of intrinsic time and semiclassical time as well as the possibility of tunneling into regions corresponding to a negative gravitational constant. We calculate the reduced density matrix of the Jordan-Brans-Dicke field and show that the off-diagonal elements can be sufficiently suppressed to be consistent with experiments. The possible relevance of this mechanism for structure formation in extended inflation is briefly discussed.Comment: 10 pages, Latex, ZU-TH 15/93, BUTP-93/1

Hawking radiation from the quantum Lemaitre-Tolman-Bondi model

In an earlier paper, we obtained exact solutions of the Wheeler-DeWitt equation for the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse, employing a lattice regularization. In this paper, we derive Hawking radiation in non-marginally bound models from our exact solutions. We show that a non-vanishing energy function does not spoil the (approximate) Planck spectrum near the horizon. We can also reliably compute corrections to the Bogoliubov coefficient because our solutions are exact. The corrections are obtained by going beyond the near horizon region and are shown to introduce additional greybody factors, which modify the black body spectrum of radiation from the black hole.Comment: 14 page

Tunneling cosmological state revisited: Origin of inflation with a non-minimally coupled Standard Model Higgs inflaton

We suggest a path integral formulation for the tunneling cosmological state, which admits a consistent renormalization and renormalization group (RG) improvement in particle physics applications of quantum cosmology. We apply this formulation to the inflationary cosmology driven by the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. In this way a complete cosmological scenario is obtained, which embraces the formation of initial conditions for the inflationary background in the form of a sharp probability peak in the distribution of the inflaton field and the ongoing generation of the Cosmic Microwave Background (CMB) spectrum on this background. Formation of this probability peak is based on the same RG mechanism which underlies the generation of the CMB spectrum which was recently shown to be compatible with the WMAP data in the Higgs mass range $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$. This brings to life a convincing unification of quantum cosmology with the particle phenomenology of the SM, inflation theory, and CMB observations.Comment: 18 pages, 3 figures, LaTe

Origin of the inflationary Universe

We give a consistent description of how the inflationary Universe emerges in quantum cosmology. This involves two steps: Firstly, it is shown that a sensible probability peak can be obtained from the cosmological wave function. This is achieved by going beyond the tree level of the semiclassical expansion. Secondly, due to decoherence interference terms between different semiclassical branches are negligibly small. The results give constraints on the particle content of a unified theory.Comment: LATEX, 6 pages, selected for honorable mention in the 1999 Essay Competition of the Gravity Research Foundation. To appear in Mod. Phys. Lett.