12 research outputs found
Effective equations for isotropic quantum cosmology including matter
Effective equations often provide powerful tools to develop a systematic
understanding of detailed properties of a quantum system. This is especially
helpful in quantum cosmology where several conceptual and technical
difficulties associated with the full quantum equations can be avoided in this
way. Here, effective equations for Wheeler-DeWitt and loop quantizations of
spatially flat, isotropic cosmological models sourced by a massive or
interacting scalar are derived and studied. The resulting systems are
remarkably different from that given for a free, massless scalar. This has
implications for the coherence of evolving states and the realization of a
bounce in loop quantum cosmology.Comment: 42 page
Coordinate time dependence in Quantum Gravity
The intuitive classical space-time picture breaks down in quantum gravity,
which makes a comparison and the development of semiclassical techniques quite
complicated. Using ingredients of the group averaging method to solve
constraints one can nevertheless introduce a classical coordinate time into the
quantum theory, and use it to investigate the way a semiclassical continuous
description emerges from discrete quantum evolution. Applying this technique to
test effective classical equations of loop cosmology and their implications for
inflation and bounces, we show that the effective semiclassical theory is in
good agreement with the quantum description even at short scales.Comment: 35 pages, 17 figure. Revised version. To appear in Phys. Rev.
Singularities in Isotropic Non-Minimal Scalar Field Models
Non-minimally coupling a scalar field to gravity introduces an additional
curvature term into the action which can change the general behavior in strong
curvature regimes, in particular close to classical singularities. While one
can conformally transform any non-minimal model to a minimally coupled one,
that transformation can itself become singular. It is thus not guaranteed that
all qualitative properties are shared by minimal and non-minimal models. This
paper addresses the classical singularity issue in isotropic models and extends
singularity removal in quantum gravity to non-minimal models.Comment: 12 page
Effective constraints of loop quantum gravity
Within a perturbative cosmological regime of loop quantum gravity corrections
to effective constraints are computed. This takes into account all
inhomogeneous degrees of freedom relevant for scalar metric modes around flat
space and results in explicit expressions for modified coefficients and of
higher order terms. It also illustrates the role of different scales
determining the relative magnitude of corrections. Our results demonstrate that
loop quantum gravity has the correct classical limit, at least in its sector of
cosmological perturbations around flat space, in the sense of perturbative
effective theory.Comment: 44 pages, 6 figure
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
Cosmological vector modes and quantum gravity effects
In contrast to scalar and tensor modes, vector modes of linear perturbations
around an expanding Friedmann--Robertson--Walker universe decay. This makes
them largely irrelevant for late time cosmology, assuming that all modes
started out at a similar magnitude at some early stage. By now, however,
bouncing models are frequently considered which exhibit a collapsing phase.
Before this phase reaches a minimum size and re-expands, vector modes grow.
Such modes are thus relevant for the bounce and may even signal the breakdown
of perturbation theory if the growth is too strong. Here, a gauge invariant
formulation of vector mode perturbations in Hamiltonian cosmology is presented.
This lays out a framework for studying possible canonical quantum gravity
effects, such as those of loop quantum gravity, at an effective level. As an
explicit example, typical quantum corrections, namely those coming from inverse
densitized triad components and holonomies, are shown to increase the growth
rate of vector perturbations in the contracting phase, but only slightly.
Effects at the bounce of the background geometry can, however, be much
stronger.Comment: 20 page
Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
Variables adapted to the quantum dynamics of spherically symmetric models are
introduced, which further simplify the spherically symmetric volume operator
and allow an explicit computation of all matrix elements of the Euclidean and
Lorentzian Hamiltonian constraints. The construction fits completely into the
general scheme available in loop quantum gravity for the quantization of the
full theory as well as symmetric models. This then presents a further
consistency check of the whole scheme in inhomogeneous situations, lending
further credence to the physical results obtained so far mainly in homogeneous
models. New applications in particular of the spherically symmetric model in
the context of black hole physics are discussed.Comment: 33 page
On Energy Conditions and Stability in Effective Loop Quantum Cosmology
In isotropic loop quantum cosmology, non-perturbatively modified dynamics of
a minimally coupled scalar field violates weak, strong and dominant energy
conditions when they are stated in terms of equation of state parameter. The
violation of strong energy condition helps to have non-singular evolution by
evading singularity theorems thus leading to a generic inflationary phase.
However, the violation of weak and dominant energy conditions raises concern,
as in general relativity these conditions ensure causality of the system and
stability of vacuum via Hawking-Ellis conservation theorem. It is shown here
that the non-perturbatively modified kinetic term contributes negative pressure
but positive energy density. This crucial feature leads to violation of energy
conditions but ensures positivity of energy density, as scalar matter
Hamiltonian remains bounded from below. It is also shown that the modified
dynamics restricts group velocity for inhomogeneous modes to remain sub-luminal
thus ensuring causal propagation across spatial distances.Comment: 29 pages, revtex4; few clarifications, references added, to appear in
CQ
Fermions in Loop Quantum Cosmology and the Role of Parity
Fermions play a special role in homogeneous models of quantum cosmology
because the exclusion principle prevents them from forming sizable matter
contributions. They can thus describe the matter ingredients only truly
microscopically and it is not possible to avoid strong quantum regimes by
positing a large matter content. Moreover, possible parity violating effects
are important especially in loop quantum cosmology whose basic object is a
difference equation for the wave function of the universe defined on a discrete
space of triads. The two orientations of a triad are interchanged by a parity
transformation, which leaves the difference equation invariant for ordinary
matter. Here, we revisit and extend loop quantum cosmology by introducing
fermions and the gravitational torsion they imply, which renders the parity
issue non-trivial. A treatable locally rotationally symmetric Bianchi model is
introduced which clearly shows the role of parity. General wave functions
cannot be parity-even or odd, and parity violating effects in matter influence
the microscopic big bang transition which replaces the classical singularity in
loop quantum cosmology.Comment: 17 page