Results 1  10
of
18
Loop quantum cosmology
, 2006
"... Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical spacetime inevitably comes to an end after a ..."
Abstract

Cited by 48 (11 self)
 Add to MetaCart
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.
Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
"... Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completel ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
(Show Context)
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed. 1
Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
, 2005
"... The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry. While the latter cannot be done in a canonical manner, it allows to consider the dynamics including the ..."
Abstract

Cited by 9 (7 self)
 Add to MetaCart
(Show Context)
The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry. While the latter cannot be done in a canonical manner, it allows to consider the dynamics including the role of small nonsymmetric degrees of freedom for the symmetric evolution. This serves as a model for the general situation of perturbative degrees of freedom in a background independent quantization such as loop quantum gravity, and for the more complicated addition of perturbative inhomogeneities. While being crucial for cosmological phenomenology, it is shown that perturbative nonsymmetric degrees of freedom do not allow definitive conclusions for the singularity issue and in such a situation could even lead to wrong claims.
Asymptotic Properties of Difference Equations for Isotropic Loop Quantum
 Cosmology, Class. Quantum Grav
"... In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler–DeWitt quantizations, and some aspects of general properties of solutions can appear differently. Properties of ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
(Show Context)
In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler–DeWitt quantizations, and some aspects of general properties of solutions can appear differently. Properties of particular interest are boundedness and the presence of smallscale oscillations. Continued fraction techniques are used to show in different matter models the presence of special initial conditions leading to bounded solutions, and an explicit expression for these initial values is derived. 1
The Volume Operator in Spherically Symmetric Quantum Geometry
, 2004
"... The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger spherically symmetric volume spectrum adds fine structure to the ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger spherically symmetric volume spectrum adds fine structure to the homogeneous spectrum. The formulas of this paper complete the derivation of an explicit calculus for spherically symmetric models which is needed for future physical investigations.
Numerical Techniques in Loop Quantum Cosmology ⋆
"... Abstract. In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve – generically, these are differen ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract. In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve – generically, these are difference (rather than differential) equations. Important issues such as differing quantization methods, stability of the solutions, the semiclassical limit, and the relevance of lattice refinement in the difference equations are discussed. Finally, the cosmological models already considered in the literature are listed, along with typical features in these models and open issues. Key words: quantum gravity; numerical techniques; loop quantum cosmology 2010 Mathematics Subject Classification: 83C45; 83Fxx; 8308 1
Inflationary universe in loop quantum cosmology
, 705
"... Abstract: Loop quantum cosmology provides a nice solution of avoiding the big bang singularity through a big bounce mechanism in the high energy region. In loop quantum cosmology an inflationary universe is emergent after the big bounce, no matter what matter component is filled in the universe. A s ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract: Loop quantum cosmology provides a nice solution of avoiding the big bang singularity through a big bounce mechanism in the high energy region. In loop quantum cosmology an inflationary universe is emergent after the big bounce, no matter what matter component is filled in the universe. A superinflation phase without phantom matter will appear in a certain way in the initial stage after the bounce; then the universe will undergo a normal inflation stage. We discuss the condition of inflation in detail in this framework. Also, for slowroll inflation, we expect the imprint from the effects of the loop quantum cosmology should be left in the primordial perturbation power spectrum. However, we show that this imprint is too weak to be observed. Contents