3,731 research outputs found
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 . 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.
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