924 research outputs found
Inhomogenous loop quantum cosmology with matter
The linearly polarized Gowdy model with a massless scalar field with
the same symmetries as the metric is quantized by applying a hybrid approach.
The homogeneous geometry degrees of freedom are loop quantized, fact which
leads to the resolution of the cosmological singularity, while a Fock
quantization is employed for both matter and gravitational inhomogeneities.
Owing to the inclusion of the massless scalar field this system allows us to
modelize flat Friedmann-Robertson-Walker cosmologies filled with
inhomogeneities propagating in one direction. It provides a perfect scenario to
study the quantum back-reaction between the inhomogeneities and the polymeric
homogeneous and isotropic background.Comment: 4 pages, Contribution to the proceedings of the Loops 11-Madrid
conferenc
Inclusion of matter in inhomogeneous loop quantum cosmology
We study the hybrid quantization of the linearly polarized Gowdy model
with a massless scalar field with the same symmetries as the metric. For
simplicity, we quantize its restriction to the model with local rotational
symmetry. Using this hybrid approach, the homogeneous degrees of freedom of the
geometry are quantized \`a la loop, leading to the resolution of the
cosmological singularity. A Fock quantization is employed both for the matter
and the gravitational inhomogeneities. Owing to the inclusion of the massless
scalar field this system allows us to modelize flat Friedmann-Robertson-Walker
cosmologies filled with inhomogeneities propagating in one direction, providing
a perfect scenario to study the quantum back-reaction of the inhomogeneities on
the polymeric homogeneous and isotropic background.Comment: 4 pages. Contribution to the Proceedings of Spanish Relativity
Meeting ERE2011, Madrid 201
Approximation methods in Loop Quantum Cosmology: From Gowdy cosmologies to inhomogeneous models in Friedmann-Robertson-Walker geometries
We develop approximation methods in the hybrid quantization of the Gowdy
model with linear polarization and a massless scalar field, for the case of
three-torus spatial topology. The loop quantization of the homogeneous
gravitational sector of the Gowdy model (according to the improved dynamics
prescription) and the presence of inhomogeneities lead to a very complicated
Hamiltonian constraint. Therefore, the extraction of physical results calls for
the introduction of well justified approximations. We first show how to
approximate the homogeneous part of the Hamiltonian constraint, corresponding
to Bianchi I geometries, as if it described a Friedmann-Robertson-Walker (FRW)
model corrected with anisotropies. This approximation is valid in the
high-energy sector of the FRW geometry (concerning its contribution to the
constraint) and for anisotropy profiles that are sufficiently smooth. In
addition, for certain families of states associated to regimes of physical
interest, with negligible effects of the anisotropies and small
inhomogeneities, one can approximate the Hamiltonian constraint of the
inhomogeneous system by that of an FRW geometry with a relatively simple matter
content, and then obtain its solutions.Comment: 20 pages, 3 figures. Minor changes, matches published versio
Hybrid Quantum Cosmology: Combining Loop and Fock Quantizations
As a necessary step towards the extraction of realistic results from Loop
Quantum Cosmology, we analyze the physical consequences of including
inhomogeneities. We consider in detail the quantization of a gravitational
model in vacuo which possesses local degrees of freedom, namely, the linearly
polarized Gowdy cosmologies with the spatial topology of a three-torus. We
carry out a hybrid quantization which combines loop and Fock techniques. We
discuss the main aspects and results of this hybrid quantization, which include
the resolution of the cosmological singularity, the polymeric quantization of
the internal time, a rigorous definition of the quantum constraints and the
construction of their solutions, the Hilbert structure of the physical states,
and the recovery of a conventional Fock quantization for the inhomogeneities.Comment: 24 pages, published in International Journal of Modern Physics A,
Special Issue: Proceedings of the Second Workshop on Quantum Gravity and
Noncommutative Geometry (Lisbon, Portugal
Modeling effective FRW cosmologies with perfect fluids from states of the hybrid quantum Gowdy model
We employ recently developed approximation methods in the hybrid quantization
of the Gowdy model with linear polarization and a massless scalar field
to obtain physically interesting solutions of this inhomogeneous cosmology.
More specifically, we propose approximate solutions of the quantum Gowdy model
constructed in such a way that, for the Hamiltonian constraint, they
effectively behave as those corresponding to a flat homogeneous and isotropic
universe filled with a perfect fluid, even though these quantum states are far
from being homogeneous and isotropic. We analyze how one can get different
perfect fluid effective behaviors, including the cases of dust, radiation, and
cosmological constant.Comment: Version accepted for publication in PR
Fermions in Hybrid Loop Quantum Cosmology
This work pioneers the quantization of primordial fermion perturbations in
hybrid Loop Quantum Cosmology (LQC). We consider a Dirac field coupled to a
spatially flat, homogeneous, and isotropic cosmology, sourced by a scalar
inflaton, and treat the Dirac field as a perturbation. We describe the
inhomogeneities of this field in terms of creation and annihilation variables,
chosen to admit a unitary evolution if the Dirac fermion were treated as a test
field. Considering instead the full system, we truncate its action at quadratic
perturbative order and construct a canonical formulation. In particular this
implies that, in the global Hamiltonian constraint of the model, the
contribution of the homogeneous sector is corrected with a quadratic
perturbative term. We then adopt the hybrid LQC approach to quantize the full
model, combining the loop representation of the homogeneous geometry with the
Fock quantization of the inhomogeneities. We assume a Born-Oppenheimer ansatz
for physical states and show how to obtain a Schr\"odinger equation for the
quantum evolution of the perturbations, where the role of time is played by the
homogeneous inflaton. We prove that the resulting quantum evolution of the
Dirac field is indeed unitary, despite the fact that the underlying homogeneous
geometry has been quantized as well. Remarkably, in such evolution, the fermion
field couples to an infinite sequence of quantum moments of the homogeneous
geometry. Moreover, the evolved Fock vacuum of our fermion perturbations is
shown to be an exact solution of the Schr\"odinger equation. Finally, we
discuss in detail the quantum backreaction that the fermion field introduces in
the global Hamiltonian constraint. For completeness, our quantum study includes
since the beginning (gauge-invariant) scalar and tensor perturbations, that
were studied in previous works.Comment: 29 pages. It matches published versio
Modified FRW cosmologies arising from states of the hybrid quantum Gowdy model
We construct approximate solutions of the hybrid quantum Gowdy cosmology with
three-torus topology, linear polarization, and local rotational symmetry, in
the presence of a massless scalar field. More specifically, we determine some
families of states for which the complicated inhomogeneous and anisotropic
Hamiltonian constraint operator of the Gowdy model is approximated by a much
simpler one. Our quantum states follow the dynamics governed by this simpler
constraint, while being at the same time also approximate solutions of the full
Gowdy model. This is so thanks to the quantum correlations that the considered
states present between the isotropic and anisotropic sectors of the model.
Remarkably, this simpler constraint can be regarded as that of a flat
Friedmann-Robertson-Walker universe filled with different kinds of perfect
fluids and geometrically corrected by homogeneous and isotropic curvature-like
terms. Therefore, our quantum states, which are intrinsically inhomogeneous,
admit approximate homogeneous and isotropic effective descriptions similar to
those considered in modified theories of gravity.Comment: Version accepted for publication in PR
Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology
Loop quantum cosmology has recently been applied in order to extend the
analysis of primordial perturbations to the Planck era and discuss the possible
effects of quantum geometry on the cosmic microwave background. Two approaches
to loop quantum cosmology with admissible ultraviolet behavior leading to
predictions that are compatible with observations are the so-called hybrid and
dressed metric approaches. In spite of their similarities and relations, we
show in this work that the effective equations that they provide for the
evolution of the tensor and scalar perturbations are somewhat different. When
backreaction is neglected, the discrepancy appears only in the time- dependent
mass term of the corresponding field equations. We explain the origin of this
difference, arising from the distinct quantization procedures. Besides, given
the privileged role that the big bounce plays in loop quantum cosmology, e.g.
as a natural instant of time to set initial conditions for the perturbations,
we also analyze the positivity of the time-dependent mass when this bounce
occurs. We prove that the mass of the tensor perturbations is positive in the
hybrid approach when the kinetic contribution to the energy density of the
inflaton dominates over its potential, as well as for a considerably large
sector of backgrounds around that situation, while this mass is always
nonpositive in the dressed metric approach. Similar results are demonstrated
for the scalar perturbations in a sector of background solutions that includes
the kinetically dominated ones; namely, the mass then is positive for the
hybrid approach, whereas it typically becomes negative in the dressed metric
case. More precisely, this last statement is strictly valid when the potential
is quadratic for values of the inflaton mass that are phenomenologically
favored.Comment: 16 pages, 3 figures. Version to be published in PR
The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology
We investigate the role played by the vacuum of the primordial fluctuations
in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton
potential is a mass term and the unperturbed quantum geometry is governed by
the effective dynamics of Loop Quantum Cosmology. In this situation, the
phenomenologically interesting solutions have a preinflationary regime where
the kinetic energy of the inflaton dominates over the potential. For these kind
of solutions, we show that the primordial power spectra depend strongly on the
choice of vacuum. We study in detail the case of adiabatic states of low order
and the non-oscillating vacuum introduced by Mart\'in de Blas and Olmedo, all
imposed at the bounce. The adiabatic spectra are typically suppressed at large
scales, and display rapid oscillations with an increase of power at
intermediate scales. In the non-oscillating vacuum, there is power suppression
for large scales, but the rapid oscillations are absent. We argue that the
oscillations are due to the imposition of initial adiabatic conditions in the
region of kinetic dominance, and that they would also be present in General
Relativity. Finally, we discuss the sensitivity of our results to changes of
the initial time and other data of the model.Comment: 29 pages, 13 figure
- …