Perfect Fluid Quantum Anisotropic Universe: Merits and Challenges

The present paper deals with quantization of perfect fluid anisotropic cosmological models. Bianchi type V and IX models are discussed following Schutz's method of expressing fluid velocities in terms of six potentials. The wave functions are found for several examples of equations of state. In one case a complete wave packet could be formed analytically. The initial singularity of a zero proper volume can be avoided in this case, but it is plagued by the usual problem of non-unitarity of anisotropic quantum cosmological models. It is seen that a particular operator ordering alleviates this problem.Comment: 13 pages, 4 figures; Accepted for publication in Gen Relativ Gravi

ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

We present a new Hamiltonian formulation of the Teleparallel Equivalent of General Relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on a spacetime. The Hamiltonian formulation is derived by means of an ADM-like 3+1 decomposition of the field and without any gauge fixing. A complete set of constraints on the phase space and their algebra are presented. The formulation is described in terms of differential forms.Comment: 43 pages, LaTeX2e; the original 73 page paper arXiv:1111.5498v1 was revised and divided into two parts. The present paper is the first part of the original one (the second part is available as arXiv:1309.4685

Condensed matter lessons about the origin of time

It is widely hoped that quantum gravity will shed light on the question of the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have naturally evolved from general relativity, on the one hand, and from particle physics, on the other hand. A third important branch of 20th century `fundamental' physics, condensed-matter physics, also offers an interesting perspective on quantum gravity, and thereby on the problem of time. The bottomline might sound disappointing: to understand the origin of time, much more experimental input is needed than what is available today. Moreover it is far from obvious that we will ever find out the true origin of physical time, even if we become able to directly probe physics at the Planck scale. But we might learn some interesting lessons about time and the structure of our universe in the process. A first lesson is that there are probably several characteristic scales associated with "quantum gravity" effects, rather than the single Planck scale usually considered. These can differ by several orders of magnitude, and thereby conspire to hide certain effects expected from quantum gravity, rendering them undetectable even with Planck-scale experiments. A more tentative conclusion is that the hierarchy between general relativity, special relativity and Newtonian physics, usually taken for granted, might have to be interpreted with caution.Comment: v1: 9 pages. Fourth juried prize in FQXi essay contest on "the Nature of Time" (2008). v2: 2015 update, partially rewritten and extended for Foundations of Physics. arXiv admin note: substantial text overlap with arXiv:0810.061

BRST Quantization of Unimodular Gravity

We study the quantization of two versions of unimodular gravity, namely fully diffeomorphism-invariant unimodular gravity and unimodular gravity with fixed metric determinant, utilizing standard path integral approach. We derive the BRST symmetry of effective actions corresponding to several relevant gauge conditions. We observe that for some gauge conditions, the restricted gauge structure may complicate the formulation and effective actions, in particular, if the chosen gauge conditions involve the canonical momentum conjugate to the induced metric on the spatial hypersurface. The BRST symmetry is extended further to the finite field-dependent BRST transformation, in order to establish the mapping between different gauge conditions in each of the two versions of unimodular gravity.Peer reviewe

Loop Quantum Cosmology

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 space-time 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 space-time 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 space-time 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 space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.Comment: 104 pages, 10 figures; online version, containing 6 movies, available at http://relativity.livingreviews.org/Articles/lrr-2005-11

Spectral action for Bianchi type-IX cosmological models

In this paper we prove a rationality phenomena for the coefficients of the heat kernel expansion of the Dirac-Laplacian of Bianchi IX cosmological models. Due the complexities arising from the anisotropic nature of the model, we present a novel method of writing the heat coefficients as Wodzicki resiudes of certain Laplacians and then provide an elegant proof of the rationality result. That is, we show that each coefficient is described by a several variable polynomial with rational coefficients of the cosmic expansion factors and their higher derivatives of a certain order. This result confirms the arithmetic nature of the complicated terms in the expansion