Tomasz Pawlowski

Anti-de Sitter universe dynamics in loop quantum cosmology

Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cient́ıficas (CSIC), Serrano 121, 28006 Madrid, Spain Institute for Gravitational Physics and Geometry, Physics Department, Penn State, University Park, PA 16802, U.S.A. Center for Gravitational Wave Physics, Physics Department, Penn State, University Park, PA 16802, U.S.A. Abstract A model for a flat isotropic universe with a negative cosmological constant Λ and a massless scalar field as sole matter content is studied within the framework of Loop Quantum Cosmology. By application of the methods introduced for the model with Λ = 0, the physical Hilbert space and the set of Dirac observables are constructed. As in that case, the scalar field plays here the role of an emergent time. The properties of the system are found to be similar to those of the k = 1 FRW model: for small energy densities, the quantum dynamics reproduces the classical one, whereas, due to modifications at near-Planckian densities, the big bang and big crunch singularities are replaced by a quantum bounce connecting deterministically the large semiclassical epochs. Thus in Loop Quantum Cosmology the evolution is qualitatively cyclic.

Time and a physical Hamiltonian for quantum gravity.

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach.

Loop quantum cosmology evolution operator of an FRW universe with a positive cosmological constant

The self-adjointness of an evolution operator {Theta}{sub {Lambda}}corresponding to the model of the flat FRW universe with massless scalar field and cosmological constant quantized in the framework of loop quantum cosmology is studied in the case {Lambda}>0. It is shown that, for {Lambda} =}{Lambda}{sub c} the operator is essentially self-adjoint, however the physical Hilbert space of the model does not contain any physically interesting states.

Positive cosmological constant in loop quantum cosmology

The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density. In the deparameterized quantum theory, the true Hamiltonian now fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach and in LQC. Irrespective of the choice of the self-adjoint extension, the big bang singularity persists in the WDW theory while it is resolved and replaced by a big bounce in loop quantum cosmology (LQC). Furthermore, the quantum evolution is surprisingly insensitive to the choice of the self-adjoint extension. This may be a special case of an yet to be discovered general property of a certain class of symmetric operators that fail to be essentially self-adjoint.

Big Bounce and inhomogeneities

The dynamics of an inhomogeneous universe is studied with the methods of loop quantum cosmology, via a so-called hybrid quantization, as an example of the quantization of vacuum cosmological spacetimes containing gravitational waves (Gowdy spacetimes). The analysis of this model with an infinite number of degrees of freedom, performed at the effective level, shows that (i) the initial Big Bang singularity is replaced (as in the case of homogeneous cosmological models) by a Big Bounce, joining deterministically two large universes, (ii) the universe size at the bounce is at least of the same order of magnitude as that of the background homogeneous universe and (iii) for each gravitational wave mode, the difference in amplitude at very early and very late times has a vanishing statistical average when the bounce dynamics is strongly dominated by the inhomogeneities, whereas this average is positive when the dynamics is in a near-vacuum regime, so that statistically the inhomogeneities are amplified.

Mechanics of multidimensional isolated horizons

Recently, a multidimensional generalization of the isolated horizon framework has been proposed (Lewandowski and Pawlowski 2005 Class. Quantum Grav. 22 1573–98). Therein the geometric description was easily generalized to higher dimensions and the structure of the constraints induced by the Einstein equations was analysed. In particular, the geometric version of the zeroth law of black-hole thermodynamics was proved. In this work, we show how the IH mechanics can be formulated in a dimension-independent fashion and derive the first law of BH thermodynamics for arbitrarily dimensional IH. We also propose a definition of energy for non-rotating horizons.

Prescriptions in loop quantum cosmology: A comparative analysis

This work was supported in part by the MICINN under Project No. FIS2008-06078-C03-03 and the Consolider-Ingenio program CPAN, under Contract No. CSD2007-00042, from Spain, and by the Natural Sciences and Engineering Research Council of Canada. T. P. acknowledges also the hospitality of the Institute of Theoretical Physics of Warsaw University and the financial support of Minister Nauki i Szkolnictwa Wyzszego under Grant No. N N202 104838. J. O. acknowledges the support of CSIC under Grant No. JAE-Pre 0800791.

Spacetimes foliated by Killing horizons

It seems to be expected that a horizon of a quasi-local type, such as a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighbourhood in the spacetime, provided the vacuum Einstein or the Einstein–Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so-called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the resulting spacetime is foliated by socalled non-expanding horizons. The obstacle is Kundt’s constraint induced at the surfaces by the Einstein or the Einstein–Maxwell equations, and the requirement that a solution be globally defined on the sphere. We derived a transformation (reflection) that creates a solution to Kundt’s constraint out of data defining an extremal isolated horizon. Using that transformation, we derived a class of exact solutions to the Einstein or Einstein–Maxwell equations of very special properties. Each spacetime we construct is foliated by a family of the Killing horizons. Moreover, it admits another, transversal Killing horizon. The intrinsic and extrinsic geometries of the transversal Killing horizon coincide with the one defined on the event horizon of the extremal Kerr–Newman solution. However, the Killing horizon in our example admits yet another Killing vector tangent to and null at it. The geometries of the leaves are given by the reflection.

Physical time and other conceptual issues of quantum gravity on the example of loop quantum cosmology

Several conceptual aspects of quantum gravity (QG) are studied on the example of the homogeneous isotropic loop quantum cosmology (LQC) model. In particular: (i) the proper time of the comoving observers is shown to be a quantum operator and a quantum spacetime metric tensor operator is derived. (ii) Solutions of the quantum scalar constraint for two different choices of the lapse function are compared and contrasted. In particular it is shown that in the case of a model with massless scalar field and cosmological constant Λ, the physical Hilbert spaces constructed for two choices of lapse are the same for Λ 0. (iii) The mechanism of the singularity avoidance is analyzed via detailed studies of an energy density operator, whose essential spectrum was shown to be an interval , where . (iv) The relation between the kinematical and the physical quantum geometry is discussed on the level of relation between observables.Several conceptual aspects of quantum gravity are studied on the example of the homogeneous isotropic LQC model. In particular:

Mechanics of higher dimensional black holes in asymptotically anti-de Sitter spacetimes

(i)