204 research outputs found
Introduction to Loop Quantum Cosmology
This is an introduction to loop quantum cosmology (LQC) reviewing mini- and
midisuperspace models as well as homogeneous and inhomogeneous effective
dynamics
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
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
On the Uniqueness of the Fock Quantization of the Dirac Field in the Closed FRW Cosmology
The Fock quantization of free fields propagating in cosmological backgrounds
is in general not unambiguously defined due to the non-stationarity of the
spacetime. For the case of a scalar field in cosmological scenarios it is known
that the criterion of unitary implementation of the dynamics serves to remove
the ambiguity in the choice of Fock representation (up to unitary equivalence).
Here, applying the same type of arguments and methods previously used for the
scalar field case, we discuss the issue of the uniqueness of the Fock
quantization of the Dirac field in the closed FRW spacetime proposed by D'Eath
and Halliwell.Comment: 11 page
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
The Effect of a positive cosmological constant on the bounce of Loop Quantum Cosmology
We provide an analytical solution to the quantum dynamics of a flat
Friedmann-Lema\^itre- Robertson-Walker model with a massless scalar field in
the presence of a small and positive cosmological constant, in the context of
Loop Quantum Cosmology. We use a perturbative treatment with respect to the
model without a cosmological constant, which is exactly solvable. Our solution
is approximate, but it is precisely valid at the high curvature regime where
quantum gravity corrections are important. We compute explicitly the evolution
of the expectation value of the volume. For semiclassical states characterized
by a Gaussian spectral profile, the introduction of a positive cosmological
constant displaces the bounce of the solvable model to lower volumes and to
higher values of the scalar field. These displacements are state dependent, and
in particular, they depend on the peak of the Gaussian profile, which measures
the momentum of the scalar field. Moreover, for those semiclassical states, the
bounce remains symmetric, as in the vanishing cosmological constant case.
However, we show that the behavior of the volume is more intricate for generic
states, leading in general to a non-symmetric bounce.Comment: 17 pages, 3 figures, v2: matches published versio
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