16 research outputs found
Closed FRW model in Loop Quantum Cosmology
The basic idea of the LQC applies to every spatially homogeneous cosmological
model, however only the spatially flat (so called ) case has been
understood in detail in the literature thus far. In the closed (so called: k=1)
case certain technical difficulties have been the obstacle that stopped the
development. In this work the difficulties are overcome, and a new LQC model of
the spatially closed, homogeneous, isotropic universe is constructed. The
topology of the spacelike section of the universe is assumed to be that of
SU(2) or SO(3). Surprisingly, according to the results achieved in this work,
the two cases can be distinguished from each other just by the local properties
of the quantum geometry of the universe. The quantum hamiltonian operator of
the gravitational field takes the form of a difference operator, where the
elementary step is the quantum of the 3-volume derived in the flat case by
Ashtekar, Pawlowski and Singh. The mathematical properties of the operator are
studied: it is essentially self-adjoint, bounded from above by 0, the 0 itself
is not an eigenvalue, the eigenvectors form a basis. An estimate on the
dimension of the spectral projection on any finite interval is provided.Comment: 19 pages, latex, no figures, high quality, nea
Prescriptions in Loop Quantum Cosmology: A comparative analysis
Various prescriptions proposed in the literature to attain the polymeric
quantization of a homogeneous and isotropic flat spacetime coupled to a
massless scalar field are carefully analyzed in order to discuss their
differences. A detailed numerical analysis confirms that, for states which are
not deep in the quantum realm, the expectation values and dispersions of some
natural observables of interest in cosmology are qualitatively the same for all
the considered prescriptions. On the contrary, the amplitude of the wave
functions of those states differs considerably at the bounce epoch for these
prescriptions. This difference cannot be absorbed by a change of
representation. Finally, the prescriptions with simpler superselection sectors
are clearly more efficient from the numerical point of view.Comment: 18 pages, 6 figures, RevTex4-1 + BibTe
Cosmic recall and the scattering picture of Loop Quantum Cosmology
The global dynamics of a homogeneous universe in Loop Quantum Cosmology is
viewed as a scattering process of its geometrodynamical equivalent. This
picture is applied to build a flexible (easy to generalize) and not restricted
just to exactly solvable models method of verifying the preservation of the
semiclassicality through the bounce. The devised method is next applied to two
simple examples: (i) the isotropic Friedman Robertson Walker universe, and (ii)
the isotropic sector of the Bianchi I model. For both of them we show, that the
dispersions in the logarithm of the volume ln(v) and scalar field momentum
ln(p_phi) in the distant future and past are related via strong triangle
inequalities. This implies in particular a strict preservation of the
semiclassicality (in considered degrees of freedom) in both the cases (i) and
(ii). Derived inequalities are general: valid for all the physical states
within the considered models.Comment: RevTex4, 19 pages, 3 figure
Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC
A general quantum constraint of the form (realized in particular in Loop Quantum Cosmology models) is
studied. Group Averaging is applied to define the Hilbert space of solutions
and the relational Dirac observables. Two cases are considered. In the first
case, the spectrum of the operator is assumed to be
discrete. The quantum theory defined by the constraint takes the form of a
Schroedinger-like quantum mechanics with a generalized Hamiltonian
. In the second case, the spectrum is absolutely continuous
and some peculiar asymptotic properties of the eigenfunctions are assumed. The
resulting Hilbert space and the dynamics are characterized by a continuous
family of the Schroedinger-like quantum theories. However, the relational
observables mix different members of the family. Our assumptions are motivated
by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases
considered in the paper correspond to the negative and, respectively, positive
cosmological constant. Our results should be also applicable in many other
general relativistic contexts.Comment: RevTex4, 32 page
Dust reference frame in quantum cosmology
We give a formulation of quantum cosmology with a pressureless dust and
arbitrary additional matter fields. The system has the property that its
Hamiltonian constraint is linear in the dust momentum. This feature provides a
natural time gauge, leading to a physical hamiltonian that is not a square
root. Quantization leads to Schr{\"o}dinger equation for which unitary
evolution is directly linked to geodesic completeness. Our approach simplifies
the analysis of both Wheeler-deWitt and loop quantum cosmology (LQC) models,
and significantly broadens the applicability of the latter. This is
demonstrated for arbitrary scalar field potential and cosmological constant in
LQC.Comment: 8 pages, iopart style + BibTe
Big Bounce and inhomogeneities
The dynamics of an inhomogeneous universe is studied with the methods of Loop
Quantum Cosmology as an example of the quantization of vacuum cosmological
spacetimes containing gravitational waves (Gowdy spacetimes). The analysis
performed at the effective level shows that: (i) The initial Big Bang
singularity is replaced (as in the case of homogeneous cosmological models) by
a Big Bounce, joining deterministically two large universes, (ii) the universe
size at the bounce is at least of the same order of magnitude as that of the
background homogeneous universe, (iii) for each gravitational wave mode, the
difference in amplitude at very early and very late times has a vanishing
statistical average when the bounce dynamics is strongly dominated by the
inhomogeneities, whereas this average is positive when the dynamics is in a
near-vacuum regime, so that statistically the inhomogeneities are amplified.Comment: RevTex4, 4 pages, 2 figure
On non-existence of static vacuum black holes with degenerate components of the event horizon
We present a simple proof of the non-existence of degenerate components of
the event horizon in static, vacuum, regular, four-dimensional black hole
spacetimes. We discuss the generalisation to higher dimensions and the
inclusion of a cosmological constant.Comment: latex2e, 9 pages in A
Inflation from non-minimally coupled scalar field in loop quantum cosmology
The FRW model with non-minimally coupled massive scalar field has been
investigated in LQC framework. Considered form of the potential and coupling
allows applications to Higgs driven inflation. Out of two frames used in the
literature to describe such systems: Jordan and Einstein frame, the latter one
is applied. Specifically, we explore the idea of the Einstein frame being the
natural 'environment' for quantization and the Jordan picture having an
emergent nature. The resulting dynamics qualitatively modifies the standard
bounce paradigm in LQC in two ways: (i) the bounce point is no longer marked by
critical matter energy density, (ii) the Planck scale physics features the
'mexican hat' trajectory with two consecutive bounces and rapid expansion and
recollapse between them. Furthermore, for physically viable coupling strength
and initial data the subsequent inflation exceeds 60 e-foldings.Comment: Clarity improved. Replaced with revised version accepted in JCA
Lattice loop quantum cosmology: scalar perturbations
We study the scalar modes of linear perturbations in loop quantum cosmology.
This is done on a lattice where each cell is taken to be homogeneous and
isotropic and can be quantized via standard homogeneous loop quantum cosmology
techniques. The appropriate interactions between nearby cells are included in
the Hamiltonian in order to obtain the correct physics. It is shown that the
quantum theory is anomaly-free: the scalar and diffeomorphism constraint
operators weakly commute with the Hamiltonian. Finally, the effective theory
encoding the leading order quantum gravity corrections is derived and is shown
to give the same holonomy-corrected effective equations that have been obtained
in previous studies.Comment: 32 pages, v2: Minor change