13 research outputs found
Observational test of inflation in loop quantum cosmology
We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulas for the scalar/tensor power spectra under the slow-roll approximation, by taking into account corrections of order higher than the runnings. We place observational bounds on the inverse-volume quantum correction \delta ~ a^{- \sigma} (\sigma >0, is the scale factor) and the slow-roll parameter \epsilon_V for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on \delta for two pivot wavenumbers k_0 for several values of \delta. The quadratic potential can be compatible with the data even in the presence of the LQC corrections, but the quartic potential is in tension with observations. We also find that the upper bounds on \delta (k_0) for given \sigma and k_0 are insensitive to the choice of the inflaton potentials
Inflationary scalar spectrum in loop quantum cosmology
In the context of loop quantum cosmology, we consider an inflationary era
driven by a canonical scalar field and occurring in the semiclassical regime,
where spacetime is a continuum but quantum gravitational effects are important.
The spectral amplitude and index of scalar perturbations on an unperturbed de
Sitter background are computed at lowest order in the slow-roll parameters. The
scalar spectrum can be blue-tilted and far from scale invariance, and tuning of
the quantization ambiguities is necessary for agreement with observations. The
results are extended to a generalized quantization scheme including those
proposed in the literature. Quantization of the matter field at sub-horizon
scales can provide a consistency check of such schemes.Comment: 29 pages, 2 figures. v2: typos corrected, discussion improved and
extended, new section added. Conclusions are unchange
Anomaly-free vector perturbations with holonomy corrections in loop quantum cosmology
We investigate vector perturbations with holonomy corrections in the
framework of loop quantum cosmology. Conditions to achieve anomaly freedom for
these perturbations are found at all orders. This requires the introduction of
counter-terms in the hamiltonian constraint. We also show that anomaly freedom
requires the diffeomorphism constraint to hold its classical form when scalar
matter is added although the issue of a vector matter source, required for full
consistency, remains to be investigated. The gauge-invariant variable and the
corresponding equation of motion are derived. The propagation of vector modes
through the bounce is finally discussed.Comment: 16 pages, 1 figure. Matches version published in Class. Quantum Gra
Early Universe Dynamics in Semi-Classical Loop Quantum Cosmology
Within the framework of loop quantum cosmology, there exists a semi-classical
regime where spacetime may be approximated in terms of a continuous manifold,
but where the standard Friedmann equations of classical Einstein gravity
receive non-perturbative quantum corrections. An approximate, analytical
approach to studying cosmic dynamics in this regime is developed for both
spatially flat and positively-curved isotropic universes sourced by a
self-interacting scalar field. In the former case, a direct correspondence
between the classical and semi-classical field equations can be established
together with a scale factor duality that directly relates different expanding
and contracting universes. Some examples of non-singular, bouncing cosmologies
are presented together with a scaling, power-law solution.Comment: 14 pages, In Press, JCA
Emergence of General Relativity from Loop Quantum Gravity
A model is proposed to demonstrate that classical general relativity can
emerge from loop quantum gravity, in a relational description of gravitational
field in terms of coordinates given by matter. Local Dirac observables and
coherent states are defined to explore physical content of the model.
Expectation values of commutators between the observables for the coherent
states recover the four-dimensional diffeomorphism algebra and the large-scale
dynamics of the gravitational field relative to the matter coordinates. Both
results conform with general relativity up to calculable corrections near
singularities.Comment: 83 pages MikteX file with 3 pdf figures. Ph.D. Thesis. Using
arbitrary real Immirzi parameter and recovering the symmetry algebra, this
work is significantly improved from its previous version. Details of the
model are also given in the conten
Loop Quantum Cosmology: A Status Report
The goal of this article is to provide an overview of the current state of
the art in loop quantum cosmology for three sets of audiences: young
researchers interested in entering this area; the quantum gravity community in
general; and, cosmologists who wish to apply loop quantum cosmology to probe
modifications in the standard paradigm of the early universe. An effort has
been made to streamline the material so that, as described at the end of
section I, each of these communities can read only the sections they are most
interested in, without a loss of continuity.Comment: 138 pages, 15 figures. Invited Topical Review, To appear in Classical
and Quantum Gravity. Typos corrected, clarifications and references adde
Observational constraints on loop quantum cosmology
In the inflationary scenario of loop quantum cosmology (LQC) in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to confront with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background (CMB) and other cosmological experiments, we place bounds on the quantum corrections for a quadratic inflaton potential