38 research outputs found
Contrasting features of anisotropic loop quantum cosmologies: the role of spatial curvature
A characteristic feature of loop quantization of the isotropic and Bianchi-I
spacetimes is the existence of universal bounds on the energy density and the
expansion and shear scalars, independent of the matter content. We investigate
the properties of these physical quantities in Bianchi-II and Bianchi-IX
spacetimes, which have been recently loop quantized using the connection
operator approach. Using the effective Hamiltonian approach, we show that for
Bianchi-II spacetime, energy density and the expansion and shear scalars turn
out to be bounded, albeit not by universal values. In Bianchi-IX spacetime,
when the approach to the classical singularity is isotropic, above physical
quantities are bounded. In addition, for all other cases, where the approach to
singularities is not isotropic and effective dynamics can be trusted, these
quantities turn out to be finite. These results stand in sharp distinction to
general relativity, where above physical quantities are generically unbounded,
leading to the break down of geodesic equations. In contrast to the isotropic
and Bianchi-I models, we find the role of energy conditions for Bianchi-II
model and the inverse triad modifications for Bianchi-IX to be significant to
obtain above bounds. These results bring out subtle physical distinctions
between the quantization using holonomies over closed loops performed for
isotropic and Bianchi-I models, and the connection operator approach. We find
that qualitative differences in physics exist for these quantization methods
even for the isotropic models in the presence of spatial curvature. We
highlight these important differences in the behavior of the expansion scalar
in the holonomy based quantization and connection operator approach for
isotropic spatially closed and open models.Comment: Minor clarifications added. To match published version in PR
Non-singular AdS-dS transitions in a landscape scenario
Understanding transitions between different vacua of a multiverse allowing
eternal inflation is an open problem whose resolution is important to gain
insights on the global structure of the spacetime as well as the problem of
measure. In the classical theory, transitions from the anti-deSitter to
deSitter vacua are forbidden due to the big crunch singularity. In this
article, we consider toy landscape potentials: a double well and a triple well
potential allowing anti-deSitter and de-Sitter vacua, in the effective dynamics
of loop quantum cosmology for the FRW model. We show that due to the
non-perturbative quantum gravity effects as understood in loop quantum
cosmology, non-singular anti-deSitter to de-Sitter transitions are possible. In
the future evolution, an anti-deSitter bubble universe does not encounter a big
crunch singularity but undergoes a big bounce occurring at a scale determined
by the underlying quantum geometry. These non-singular transitions provide a
mechanism through which a probe or a `watcher', used to define a local measure,
can safely evolve through the bounce and geodesics can be smoothly extended
from anti-deSitter to de-Sitter vacua.Comment: Revised version. Appendix on results in k=0 model added. To appear in
PR
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