16 research outputs found
Renormalization Group Flow in CDT
We perform a first investigation of the coupling constant flow of the
nonperturbative lattice model of four-dimensional quantum gravity given in
terms of Causal Dynamical Triangulations (CDT). After explaining how standard
concepts of lattice field theory can be adapted to the case of this
background-independent theory, we define a notion of "lines of constant
physics" in coupling constant space in terms of certain semiclassical
properties of the dynamically generated quantum universe. Determining flow
lines with the help of Monte Carlo simulations, we find that the second-order
phase transition line present in this theory can be interpreted as a UV phase
transition line if we allow for an anisotropic scaling of space and time.Comment: Typos corrected, 21 page
Spherically symmetric Einstein-Maxwell theory and loop quantum gravity corrections
Effects of inverse triad corrections and (point) holonomy corrections,
occuring in loop quantum gravity, are considered on the properties of
Reissner-Nordstr\"om black holes. The version of inverse triad corrections with
unmodified constraint algebra reveals the possibility of occurrence of three
horizons (over a finite range of mass) and also shows a mass threshold beyond
which the inner horizon disappears. For the version with modified constraint
algebra, coordinate transformations are no longer a good symmetry. The
covariance property of spacetime is regained by using a \emph{quantum} notion
of mapping from phase space to spacetime. The resulting quantum effects in both
versions of these corrections can be associated with renormalization of either
mass, charge or wave function. In neither of the versions, Newton's constant is
renormalized. (Point) Holonomy corrections are shown to preclude the undeformed
version of constraint algebra as also a static solution, though
time-independent solutions exist. A possible reason for difficulty in
constructing a covariant metric for these corrections is highlighted.
Furthermore, the deformed algebra with holonomy corrections is shown to imply
signature change.Comment: 38 pages, 9 figures, matches published versio
Polymer quantization of the free scalar field and its classical limit
Building on prior work, a generally covariant reformulation of free scalar
field theory on the flat Lorentzian cylinder is quantized using Loop Quantum
Gravity (LQG) type `polymer' representations. This quantization of the {\em
continuum} classical theory yields a quantum theory which lives on a discrete
spacetime lattice. We explicitly construct a state in the polymer Hilbert space
which reproduces the standard Fock vacuum- two point functions for long
wavelength modes of the scalar field. Our construction indicates that the
continuum classical theory emerges under coarse graining. All our
considerations are free of the "triangulation" ambiguities which plague
attempts to define quantum dynamics in LQG. Our work constitutes the first
complete LQG type quantization of a generally covariant field theory together
with a semi-classical analysis of the true degrees of freedom and thus provides
a perfect infinite dimensional toy model to study open issues in LQG,
particularly those pertaining to the definition of quantum dynamics.Comment: 58 page
Modified general relativity as a model for quantum gravitational collapse
We study a class of Hamiltonian deformations of the massless
Einstein-Klein-Gordon system in spherical symmetry for which the Dirac
constraint algebra closes. The system may be regarded as providing effective
equations for quantum gravitational collapse. Guided by the observation that
scalar field fluxes do not follow metric null directions due to the
deformation, we find that the equations take a simple form in characteristic
coordinates. We analyse these equations by a unique combination of numerical
methods and find that Choptuik's mass scaling law is modified by a mass gap as
well as jagged oscillations. Furthermore, the results are universal with
respect to different initial data profiles and robust under changes of the
deformation.Comment: 22 pages, 4 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
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
Numerical simulation of skin transport using Parareal
In silico investigation of skin permeation is an important but also computationally demanding problem. To resolve all scales involved in full detail will not only require exascale computing capacities but also suitable parallel algorithms. This article investigates the applicability of the time-parallel Parareal algorithm to a brick and mortar setup, a precursory problem to skin permeation. The C++ library Lib4PrM implementing Parareal is combined with the UG4 simulation framework, which provides the spatial discretization and parallelization. The combination’s performance is studied with respect to convergence and speedup. It is confirmed that anisotropies in the domain and jumps in diffusion coefficients only have a minor impact on Parareal’s convergence. The influence of load imbalances in time due to differences in number of iterations required by the spatial solver as well as spatio-temporal weak scaling is discussed
Singularity resolution from polymer quantum matter
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