512 research outputs found
Initial Conditions for a Universe
In physical theories, boundary or initial conditions play the role of
selecting special situations which can be described by a theory with its
general laws. Cosmology has long been suspected to be different in that its
fundamental theory should explain the fact that we can observe only one
particular realization. This is not realized, however, in the classical
formulation and in its conventional quantization; the situation is even worse
due to the singularity problem. In recent years, a new formulation of quantum
cosmology has been developed which is based on quantum geometry, a candidate
for a theory of quantum gravity. Here, the dynamical law and initial conditions
turn out to be linked intimately, in combination with a solution of the
singularity problem.Comment: 7 pages, this essay was awarded First Prize in the Gravity Research
Foundation Essay Contest 200
Quantum gravity, space-time structure, and cosmology
A set of diverse but mutually consistent results obtained in different
settings has spawned a new view of loop quantum gravity and its physical
implications, based on the interplay of operator calculations and effective
theory: Quantum corrections modify, but do not destroy, space-time and the
notion of covariance. Potentially observable effects much more promising than
those of higher-curvature effective actions result; loop quantum gravity has
turned into a falsifiable framework, with interesting ingredients for new
cosmic world views. At Planckian densities, space-time disappears and is
replaced by 4-dimensional space without evolution.Comment: 8 pages, 7 figures, Plenary talk at CosGrav12, held at Indian
Statistical Institute, Kolkat
Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
The relation between an isotropic and an anisotropic model in loop quantum
cosmology is discussed in detail, comparing the strict symmetry reduction with
a perturbative implementation of symmetry. While the latter cannot be done in a
canonical manner, it allows to consider the dynamics including the role of
small non-symmetric degrees of freedom for the symmetric evolution. This serves
as a model for the general situation of perturbative degrees of freedom in a
background independent quantization such as loop quantum gravity, and for the
more complicated addition of perturbative inhomogeneities. While being crucial
for cosmological phenomenology, it is shown that perturbative non-symmetric
degrees of freedom do not allow definitive conclusions for the singularity
issue and in such a situation could even lead to wrong claims.Comment: 32 page
Loop Quantum Cosmology: Recent Progress
Aspects of the full theory of loop quantum gravity can be studied in a
simpler context by reducing to symmetric models like cosmological ones. This
leads to several applications where loop effects play a significant role when
one is sensitive to the quantum regime. As a consequence, the structure of and
the approach to classical singularities are very different from general
relativity: The quantum theory is free of singularities, and there are new
phenomenological scenarios for the evolution of the very early universe
including inflation. We give an overview of the main effects, focussing on
recent results obtained by several different groups.Comment: 17 pages, 2 figures, Plenary talk at ICGC 04, Cochin, Indi
Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum Gravity
Degenerate geometrical configurations in quantum gravity are important to
understand if the fate of classical singularities is to be revealed. However,
not all degenerate configurations arise on an equal footing, and one must take
into account dynamical aspects when interpreting results: While there are many
degenerate spatial metrics, not all of them are approached along the dynamical
evolution of general relativity or a candidate theory for quantum gravity. For
loop quantum gravity, relevant properties and steps in an analysis are
summarized and evaluated critically with the currently available information,
also elucidating the role of degrees of freedom captured in the sector provided
by loop quantum cosmology. This allows an outlook on how singularity removal
might be analyzed in a general setting and also in the full theory. The general
mechanism of loop quantum cosmology will be shown to be insensitive to recently
observed unbounded behavior of inverse volume in the full theory. Moreover,
significant features of this unboundedness are not a consequence of
inhomogeneities but of non-Abelian effects which can also be included in
homogeneous models.Comment: 28 pages, 1 figure; v2: extended discussion of singularity removal
and summar
Homogeneous Loop Quantum Cosmology
Loop quantum cosmological methods are extended to homogeneous models in
diagonalized form. It is shown that the diagonalization leads to a
simplification of the volume operator such that its spectrum can be determined
explicitly. This allows the calculation of composite operators, most
importantly the Hamiltonian constraint. As an application the dynamics of the
Bianchi I model is studied and it is shown that its loop quantization is free
of singularities.Comment: 25 pages, 3 figure
A no-singularity scenario in loop quantum gravity
Canonical methods allow the derivation of effective gravitational actions
from the behavior of space-time deformations reflecting general covariance.
With quantum effects, the deformations and correspondingly the effective
actions change, revealing dynamical implications of quantum corrections. A new
systematic way of expanding these actions is introduced showing as a first
result that inverse-triad corrections of loop quantum gravity simplify the
asymptotic dynamics near a spacelike collapse singularity. By generic quantum
effects, the singularity is removed.Comment: 10 page
Hubble operator in isotropic loop quantum cosmology
We present a construction of the Hubble operator for the spatially flat
isotropic loop quantum cosmology. This operator is a Dirac observable on a
subspace of the space of physical solutions. This subspace gets selected
dynamically, requiring that its action be invariant on the physical solution
space. As a simple illustrative application of the expectation value of the
operator, we do find a generic phase of (super)inflation, a feature shown by
Bojowald from the analysis of effective Friedmann equation of loop quantum
cosmology.Comment: 20 pages, 3 eps figures, few comments and clarifications added to
match with the published versio
The Early Universe in Loop Quantum Cosmology
Loop quantum cosmology applies techniques derived for a background
independent quantization of general relativity to cosmological situations and
draws conclusions for the very early universe. Direct implications for the
singularity problem as well as phenomenology in the context of inflation or
bouncing universes result, which will be reviewed here. The discussion focuses
on recent new results for structure formation and generalizations of the
methods.Comment: 10 pages, 3 figures, plenary talk at VI Mexican School on Gravitation
and Mathematical Physics, Nov 21-27, 200
Loop Quantum Cosmology III: Wheeler-DeWitt Operators
In the framework of loop quantum cosmology anomaly free quantizations of the
Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and
isotropic models are given. Basic ideas of the construction in (non-symmetric)
loop quantum gravity can be used, but there are also further inputs because the
special structure of symmetric models has to be respected by operators. In
particular, the basic building blocks of the homogeneous models are point
holonomies rather than holonomies necessitating a new regularization procedure.
In this respect, our construction is applicable also for other
(non-homogeneous) symmetric models, e.g. the spherically symmetric one.Comment: 19 page
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