7 research outputs found
The Quantum Configuration Space of Loop Quantum Cosmology
The article gives an account of several aspects of the space known as the
Bohr compactification of the line, featuring as the quantum configuration space
in loop quantum cosmology, as well as of the corresponding configuration space
realization of the so-called polymer representation. Analogies with loop
quantum gravity are explored, providing an introduction to (part of) the
mathematical structure of loop quantum gravity, in a technically simpler
context.Comment: 14 pages. Minor changes, typos corrected, 1 reference added. To
appear in Class. Quantum Gra
Numerical loop quantum cosmology: an overview
A brief review of various numerical techniques used in loop quantum cosmology
and results is presented. These include the way extensive numerical simulations
shed insights on the resolution of classical singularities, resulting in the
key prediction of the bounce at the Planck scale in different models, and the
numerical methods used to analyze the properties of the quantum difference
operator and the von Neumann stability issues. Using the quantization of a
massless scalar field in an isotropic spacetime as a template, an attempt is
made to highlight the complementarity of different methods to gain
understanding of the new physics emerging from the quantum theory. Open
directions which need to be explored with more refined numerical methods are
discussed.Comment: 33 Pages, 4 figures. Invited contribution to appear in Classical and
Quantum Gravity special issue on Non-Astrophysical Numerical Relativit
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
On (Cosmological) Singularity Avoidance in Loop Quantum Gravity
Loop Quantum Cosmology (LQC), mainly due to Bojowald, is not the cosmological
sector of Loop Quantum Gravity (LQG). Rather, LQC consists of a truncation of
the phase space of classical General Relativity to spatially homogeneous
situations which is then quantized by the methods of LQG. Thus, LQC is a
quantum mechanical toy model (finite number of degrees of freedom) for LQG(a
genuine QFT with an infinite number of degrees of freedom) which provides
important consistency checks. However, it is a non trivial question whether the
predictions of LQC are robust after switching on the inhomogeneous fluctuations
present in full LQG. Two of the most spectacular findings of LQC are that 1.
the inverse scale factor is bounded from above on zero volume eigenstates which
hints at the avoidance of the local curvature singularity and 2. that the
Quantum Einstein Equations are non -- singular which hints at the avoidance of
the global initial singularity. We display the result of a calculation for LQG
which proves that the (analogon of the) inverse scale factor, while densely
defined, is {\it not} bounded from above on zero volume eigenstates. Thus, in
full LQG, if curvature singularity avoidance is realized, then not in this
simple way. In fact, it turns out that the boundedness of the inverse scale
factor is neither necessary nor sufficient for curvature singularity avoidance
and that non -- singular evolution equations are neither necessary nor
sufficient for initial singularity avoidance because none of these criteria are
formulated in terms of observable quantities.After outlining what would be
required, we present the results of a calculation for LQG which could be a
first indication that our criteria at least for curvature singularity avoidance
are satisfied in LQG.Comment: 34 pages, 16 figure