26 research outputs found
Loop Quantization of Vacuum Bianchi I Cosmology
We analyze the loop quantization of the family of vacuum Bianchi I
spacetimes, a gravitational system whose classical solutions describe
homogeneous anisotropic cosmologies. We rigorously construct the operator that
represents the Hamiltonian constraint, showing that the states of zero volume
completely decouple from the rest of quantum states. This fact ensures that the
classical cosmological singularity is resolved in the quantum theory. In
addition, this allows us to adopt an equivalent quantum description in terms of
a well defined densitized Hamiltonian constraint. This latter constraint can be
regarded in a certain sense as a difference evolution equation in an internal
time provided by one of the triad components, which is polymerically quantized.
Generically, this evolution equation is a relation between the projection of
the quantum states in three different sections of constant internal time.
Nevertheless, around the initial singularity the equation involves only the two
closest sections with the same orientation of the triad. This has a double
effect: on the one hand, physical states are determined just by the data on one
section, on the other hand, the evolution defined in this way never crosses the
singularity, without the need of any special boundary condition. Finally, we
provide these physical states with a Hilbert structure, completing the
quantization.Comment: 10 pages, version accepted for publication in Physical Review
On Unitary Time Evolution in Gowdy Cosmologies
A non-perturbative canonical quantization of Gowdy polarized models
carried out recently is considered. This approach profits from the equivalence
between the symmetry reduced model and 2+1 gravity coupled to a massless real
scalar field. The system is partially gauge fixed and a choice of internal time
is performed, for which the true degrees of freedom of the model reduce to a
massless free scalar field propagating on a 2-dimensional expanding torus. It
is shown that the symplectic transformation that determines the classical
dynamics cannot be unitarily implemented on the corresponding Hilbert space of
quantum states. The implications of this result for both quantization of fields
on curved manifolds and physically relevant questions regarding the initial
singularity are discussed.Comment: 16 pages, no figures, latex file; references added, a proof included.
Final version to appear in IJMP
Hierarchy and Wave Functions in a Simple Quantum Cosmology
Astrophysical observations indicate the expansion of the universe is
accelerating. Applying the holographic entropy conjecture to the cosmological
horizon in an accelerating universe suggests the universe has only a finite
number of degrees of freedom. This is consistent with a closed universe arising
from a quantum fluctuation, with zero total quantum numbers. If space-time has
eleven dimensions, and the universe began as a closed force-symmetric
ten-dimensional space with characteristic dimension L, seven of the space
dimensions must have collapsed to generate the three large space dimensions we
see. The holographic conjecture then suggests the initial length scale L must
be roughly twenty orders of magnitude larger than the Planck length.
Accordingly, the nuclear force must be roughly forty orders of magnitude
stronger than gravity, possibly resolving the force hierarchy problem. A
wavefunction for the radius of curvature of the universe can be obtained from
the Schrodinger equation derived by Elbaz and Novello. The product of this
wavefunction and its complex conjugate can be interpreted as the probability
density for finding a given radius of curvature in one of the infinity of
measurements of the radius of curvature possible (in principle) at any location
in a homogeneous isotropic universe.Comment: 4 pages, no figures, abstract corrected to insert omitted word
Loop Quantum Cosmology: A cosmological theory with a view
Loop Quantum Gravity is a background independent, nonperturbative approach to
the quantization of General Relativity. Its application to models of interest
in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new
and exciting views of the gravitational phenomena that took place in the early
universe, or that occur in spacetime regions where Einstein's theory predicts
singularities. We provide a brief introduction to the bases of Loop Quantum
Cosmology and summarize the most important results obtained in homogeneous
scenarios. These results include a mechanism to avoid the cosmological Big Bang
singularity and replace it with a Big Bounce, as well as the existence of
processes which favor inflation. We also discuss the extension of the frame of
Loop Quantum Cosmology to inhomogeneous settings.Comment: 17 pages, to appear in Proceedings of Spanish Relativity Meeting 2010
(ERE 2010) held in Granada, Spai
On the Schroedinger Representation for a Scalar Field on Curved Spacetime
It is generally known that linear (free) field theories are one of the few
QFT that are exactly soluble. In the Schroedinger functional description of a
scalar field on flat Minkowski spacetime and for flat embeddings, it is known
that the usual Fock representation is described by a Gaussian measure. In this
paper, arbitrary globally hyperbolic space-times and embeddings of the Cauchy
surface are considered. The classical structures relevant for quantization are
used for constructing the Schroedinger representation in the general case. It
is shown that in this case, the measure is also Gaussian. Possible implications
for the program of canonical quantization of midisuperspace models are pointed
out.Comment: 11 pages, Revtex, no figure
The linearization of the Kodama state
We study the question of whether the linearization of the Kodama state around
classical deSitter spacetime is normalizable in the inner product of the theory
of linearized gravitons on deSitter spacetime. We find the answer is no in the
Lorentzian theory. However, in the Euclidean theory the corresponding
linearized Kodama state is delta-functional normalizable. We discuss whether
this result invalidates the conjecture that the full Kodama state is a good
physical state for quantum gravity with positive cosmological constant.Comment: 14 pages, statement on the corresponding Yang-Mills case correcte
Higher-Derivative Quantum Cosmology
The quantum cosmology of a higher-derivative derivative gravity theory
arising from the heterotic string effective action is reviewed. A new type of
Wheeler-DeWitt equation is obtained when the dilaton is coupled to the
quadratic curvature terms. Techniques for solving the Wheeler-DeWitt equation
with appropriate boundary conditions shall be described, and implications for
semiclassical theories of inflationary cosmology will be outlined.Comment: 11 pages TeX. A term has been removed from equation (13
Is there a problem with quantum wormhole states in N=1 Supergravity?
The issue concerning the existence of wormhole states in locally
supersymmetric minisuperspace models with matter is addressed. Wormhole states
are apparently absent in models obtained from the more general theory of N=1
supergravity with supermatter. A Hartle-Hawking type solution can be found,
even though some terms (which are scalar field dependent) cannot be determined
in a satisfactory way. A possible cause is investigated here. As far as the
wormhole situation is concerned, we argue here that the type of Lagrange
multipliers and fermionic derivative ordering used can make a difference. A
proposal is made for supersymmetric quantum wormholes to also be invested with
a Hilbert space structure, associated with a maximal analytical extension of
the corresponding minisuperspace.is concerned, we argue here that the type of
Lagrange multipliers and fermionic derivative ordering used can make a
difference. A proposal is made for supersymmetric quantum wormholes to also be
invested with a Hilbert space structure, associated with a maximal analytical
extension of the corresponding minisuperspace.Comment: 22 pages, TeX (some font problems may occur, just press Return),
Based on a essay submitted to the 1995 ravity Research Foundation Awards,
accepted in G.R.
Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies
Heuristic arguments and numerical simulations support the Belinskii et al
(BKL) claim that the approach to the singularity in generic gravitational
collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to
identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By
writing the metric of one spacetime in the standard variables of another,
signatures for LMD may be found. Such signatures for the dynamics of spatially
homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are
reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the
dynamics of generic -symmetric spacetime are presented.Comment: 17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime
Safari: Essays in Honour of Vincent Moncrief