582 research outputs found
Chimera: A hybrid approach to numerical loop quantum cosmology
The existence of a quantum bounce in isotropic spacetimes is a key result in
loop quantum cosmology (LQC), which has been demonstrated to arise in all the
models studied so far. In most of the models, the bounce has been studied using
numerical simulations involving states which are sharply peaked and which
bounce at volumes much larger than the Planck volume. An important issue is to
confirm the existence of the bounce for states which have a wide spread, or
which bounce closer to the Planck volume. Numerical simulations with such
states demand large computational domains, making them very expensive and
practically infeasible with the techniques which have been implemented so far.
To overcome these difficulties, we present an efficient hybrid numerical scheme
using the property that at the small spacetime curvature, the quantum
Hamiltonian constraint in LQC, which is a difference equation with uniform
discretization in volume, can be approximated by a Wheeler-DeWitt differential
equation. By carefully choosing a hybrid spatial grid allowing the use of
partial differential equations at large volumes, and with a simple change of
geometrical coordinate, we obtain a surprising reduction in the computational
cost. This scheme enables us to explore regimes which were so far unachievable
for the isotropic model in LQC. Our approach also promises to significantly
reduce the computational cost for numerical simulations in anisotropic LQC
using high performance computing.Comment: Minor revision to match published version. To appear in CQ
Numerical simulations of a loop quantum cosmos: robustness of the quantum bounce and the validity of effective dynamics
A key result of isotropic loop quantum cosmology is the existence of a
quantum bounce which occurs when the energy density of the matter field
approaches a universal maximum close to the Planck density. Though the bounce
has been exhibited in various matter models, due to severe computational
challenges some important questions have so far remained unaddressed. These
include the demonstration of the bounce for widely spread states, its detailed
properties for the states when matter field probes regions close to the Planck
volume and the reliability of the continuum effective spacetime description in
general. In this manuscript we rigorously answer these questions using the
Chimera numerical scheme for the isotropic spatially flat model sourced with a
massless scalar field. We show that as expected from an exactly solvable model,
the quantum bounce is a generic feature of states even with a very wide spread,
and for those which bounce much closer to the Planck volume. We perform a
detailed analysis of the departures from the effective description and find
some expected, and some surprising results. At a coarse level of description,
the effective dynamics can be regarded as a good approximation to the
underlying quantum dynamics unless the states correspond to small scalar field
momenta, in which case they bounce closer to the Planck volume, or are very
widely spread. Quantifying the amount of discrepancy between the quantum and
the effective dynamics, we find that the departure between them depends in a
subtle and non-monotonic way on the field momentum and different fluctuations.
Interestingly, the departures are generically found to be such that the
effective dynamics overestimates the spacetime curvature, and underestimates
the volume at the bounce.Comment: 47 pages, 26 figures; References updated. Minor changes to match the
version published in CQ
Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology
In recent years, numerical simulations with Gaussian initial states have
demonstrated the existence of a quantum bounce in loop quantum cosmology in
various models. A key issue pertaining to the robustness of the bounce and the
associated physics is to understand the quantum evolution for more general
initial states which may depart significantly from Gaussianity and may have no
well defined peakedness properties. The analysis of such states, including
squeezed and highly non-Gaussian states, has been computationally challenging
until now. In this manuscript, we overcome these challenges by using the
Chimera scheme for the spatially flat, homogeneous and isotropic model sourced
with a massless scalar field. We demonstrate that the quantum bounce in this
model occurs even for states which are highly squeezed or are non-Gaussian with
multiple peaks and with little resemblance to semi-classical states. The
existence of the bounce is found to be robust, being independent of the
properties of the states. The evolution of squeezed and non-Gaussian states
turns out to be qualitatively similar to that of Gaussian states, and satisfies
strong constraints on the growth of the relative fluctuations across the
bounce. We also compare the results from the effective dynamics and find that,
although it captures the qualitative aspects of the evolution for squeezed and
highly non-Gaussian states, it always underestimates the bounce volume. We show
that various properties of the evolution, such as the energy density at the
bounce, are in excellent agreement with the predictions from an exactly
solvable loop quantum cosmological model for arbitrary states.Comment: 26 pages, 16 figures. v2: Discussion of the main results expande
Self-force with (3+1) codes: a primer for numerical relativists
Prescriptions for numerical self-force calculations have traditionally been
designed for frequency-domain or (1+1) time-domain codes which employ a mode
decomposition to facilitate in carrying out a delicate regularization scheme.
This has prevented self-force analyses from benefiting from the powerful suite
of tools developed and used by numerical relativists for simulations of the
evolution of comparable-mass black hole binaries. In this work, we revisit a
previously-introduced (3+1) method for self-force calculations, and demonstrate
its viability by applying it to the test case of a scalar charge moving in a
circular orbit around a Schwarzschild black hole. Two (3+1) codes originally
developed for numerical relativity applications were independently employed,
and in each we were able to compute the two independent components of the
self-force and the energy flux correctly to within . We also demonstrate
consistency between -component of the self-force and the scalar energy flux.
Our results constitute the first successful calculation of a self-force in a
(3+1) framework, and thus open opportunities for the numerical relativity
community in self-force analyses and the perturbative modeling of
extreme-mass-ratio inspirals.Comment: 23 pages, 13 figure
A multi-block infrastructure for three-dimensional time-dependent numerical relativity
We describe a generic infrastructure for time evolution simulations in
numerical relativity using multiple grid patches. After a motivation of this
approach, we discuss the relative advantages of global and patch-local tensor
bases. We describe both our multi-patch infrastructure and our time evolution
scheme, and comment on adaptive time integrators and parallelisation. We also
describe various patch system topologies that provide spherical outer and/or
multiple inner boundaries.
We employ penalty inter-patch boundary conditions, and we demonstrate the
stability and accuracy of our three-dimensional implementation. We solve both a
scalar wave equation on a stationary rotating black hole background and the
full Einstein equations. For the scalar wave equation, we compare the effects
of global and patch-local tensor bases, different finite differencing
operators, and the effect of artificial dissipation onto stability and
accuracy. We show that multi-patch systems can directly compete with the
so-called fixed mesh refinement approach; however, one can also combine both.
For the Einstein equations, we show that using multiple grid patches with
penalty boundary conditions leads to a robustly stable system. We also show
long-term stable and accurate evolutions of a one-dimensional non-linear gauge
wave. Finally, we evolve weak gravitational waves in three dimensions and
extract accurate waveforms, taking advantage of the spherical shape of our grid
lines.Comment: 18 pages. Some clarifications added, figure layout improve
Turduckening black holes: an analytical and computational study
We provide a detailed analysis of several aspects of the turduckening
technique for evolving black holes. At the analytical level we study the
constraint propagation for a general family of BSSN-type formulation of
Einstein's field equations and identify under what conditions the turducken
procedure is rigorously justified and under what conditions constraint
violations will propagate to the outside of the black holes. We present
high-resolution spherically symmetric studies which verify our analytical
predictions. Then we present three dimensional simulations of single distorted
black holes using different variations of the turduckening method and also the
puncture method. We study the effect that these different methods have on the
coordinate conditions, constraint violations, and extracted gravitational
waves. We find that the waves agree up to small but non-vanishing differences,
caused by escaping superluminal gauge modes. These differences become smaller
with increasing detector location.Comment: Minor changes to match the final version to appear in PR
Accelerated motion and the self-force in Schwarzschild spacetime
We provide expansions of the Detweiler-Whiting singular field for motion
along arbitrary, planar accelerated trajectories in Schwarzschild spacetime. We
transcribe these results into mode-sum regularization parameters, computing
previously unknown terms that increase the convergence rate of the mode-sum. We
test our results by computing the self-force along a variety of accelerated
trajectories. For non-uniformly accelerated circular orbits we present results
from a new 1+1D discontinuous Galerkin time-domain code which employs an
effective-source. We also present results for uniformly accelerated circular
orbits and accelerated bound eccentric orbits computed within a
frequency-domain treatment. Our regularization results will be useful for
computing self-consistent self-force inspirals where the particle's worldline
is accelerated with respect to the background spacetime.Comment: 19 pages, 6 figures (accepted CQG special issue article version
Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis
We extract a quantitative variant of uniqueness from the usual hypotheses of the implicit functions theorem. This leads not only to an a priori proof of continuity, but also to an alternative, fully constructive existence proof
A Lightweight Field Cage for a Large TPC Prototype for the ILC
We have developed and constructed the field cage of a prototype Time
Projection Chamber for research and development studies for a detector at the
International Linear Collider. This prototype has an inner diameter of 72 cm
and a length of 61 cm. The design of the field cage wall was optimized for a
low material budget of 1.21 % of a radiation length and a drift field
homogeneity of Delta(E)/(E) less or equal 10^-4. Since November 2008 the
prototype has been part of a comprehensive test beam setup at DESY and used as
a test chamber for the development of Micro Pattern Gas Detector based readout
devices.Comment: 16 pages, 13 figures, 3 table
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