Formation and evolution of structure in loop cosmology

Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections, in particular, in gravitational parts. This provides a framework for calculating the evolution of modes in structure formation scenarios related to inflationary or bouncing models. Applications here are corrections to the Newton potential and to the evolution of large scale modes which imply nonconservation of curvature perturbations possibly noticeable in a running spectral index. These effects are sensitive to quantization procedures and test the characteristic behavior of correction terms derived from quantum gravity.     

Classical and quantum Hořava–Lifshitz cosmology in a minisuperspace perspective

We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology in the framework of the gravity theory proposed by Ho?ava, the so-called Ho?ava–Lifshitz theory of gravity. Beginning with the ADM representation of the action corresponding to this model, we construct the Lagrangian in terms of the minisuperspace variables and show that in comparison with the usual Einstein-Hilbert gravity, there are some correction terms coming from the Ho?ava theory. Either in the matter free or in the case when the considered universe is filled with a perfect fluid, the exact solutions to the classical field equations are obtained for the flat, closed and open FRW model and some discussions about their possible singularities are presented. We then deal with the quantization of the model in the context of the Wheeler–DeWitt approach of quantum cosmology to find the cosmological wave function. We use the resulting wave functions to investigate the possibility of the avoidance of classical singularities due to quantum effects.     

A perturbative approach to chiral induced two-dimensional gravity

In the framework of the covariant approach, based on perturbation theory, two-dimensional chiral induced quantum gravity is analyzed. The quantum equivalence with the local version of two-dimensional induced quantum gravity is established.Lenin Komsemol Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 102–105, December, 1992.     

How quantum is the big bang?

When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective equations are derived for isotropic models with an interacting scalar to all orders in the expansions involved. The resulting coupling terms show that quantum fluctuations do not affect the bounce much. Quantum correlations, however, do have an important role and could even eliminate the bounce. How quantum gravity regularizes the big bang depends crucially on properties of the quantum state.     

<Emphasis Type="Italic">q</Emphasis>-plane-wave solutions of <Emphasis Type="Italic">q</Emphasis>-Weyl gravity

The solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves are given. The text was submitted by the authors in English.     

Quantum cosmology and stationary states

A model for quantum gravity, in which the conformal part of the metric is quantized using the path integral formalism, is presented. Einstein's equations can be suitably modified to take into account the effects of quantum conformal fluctuations. A closed Friedman model can be described in terms of well-defined stationary states. The “ground state” sets a lower bound (at Planck length) to the scale factor preventing the collapse. A possible explanation for matter creation and quantum nature of matter is suggested.     

One-loop counterterms in 2d dilaton-Maxwell quantum gravity

The renormalization structure of two-dimensional quantum gravity is investigated in a covariant gauge. One-loop divergences of the effective action are calculated. All the surface divergent terms are taken into account thus completing previous one-loop calculations of the theory. It is shown that the on-shell effective action contains only surface divergences. The off-shell renormalizability of the theory is discussed and classes of renormalizable dilaton and Maxwell potentials are found.     

Random surfaces in three-dimensional simplicial gravity

A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of three-dimensional DT manifold with topology. A new scaling behavior of genus distributions of boundary surfaces is found. Furthermore, these surfaces are compared with the random surfaces generated by the two-dimensional DT method which are well known as a correct discretized method of the two-dimensional quantum gravity.     

Conformal Invariance and Gravitational Coupling in Quantum Field Theory

We study the quantum constraints of a conformalinvariant action for a scalar field. For this purpose webriefly present a reformulation of the duality principleadvanced earlier in the context of generally covariant quantum field theory, and apply it toexamine the finite structure of the quantum constraints.This structure is shown to admit a dimensional coupling(a coupling mediated by a dimensional coupling parameter) of states to gravity. Invariancebreaking is introduced by defining a preferredconfiguration of dynamical variables in terms of thelargescale characteristics of the universe. In thisconfiguration a close relationship between the quantumconstraints and the Einstein equations isestablished.     

A matrix model for 2D quantum gravity defined by Causal dynamical triangulations

A novel continuum theory of two-dimensional quantum gravity, based on a version of Causal Dynamical Triangulations which incorporates topology change, has recently been formulated as a genuine string field theory in zero-dimensional target space [J. Ambjørn, R. Loll, Y. Watabiki, W. Westra, S. Zohren, arXiv: 0802.0719]. Here we show that the Dyson–Schwinger equations of this string field theory are reproduced by a cubic matrix model. This matrix model also appears in the so-called Dijkgraaf–Vafa correspondence if the superpotential there is required to be renormalizable. In the spirit of this model, as well as the original large-N expansion by 't Hooft, we need no special double-scaling limit involving a fine tuning of coupling constants to obtain the continuum quantum-gravitational theory. Our result also implies a matrix model representation of the original, strictly causal quantum gravity model.     

Tunneling through bridges: Bohmian non-locality from higher-derivative gravity

A classical origin for the Bohmian quantum potential, as that potential term arises in the quantum mechanical treatment of black holes and Einstein–Rosen (ER) bridges, can be based on 4th-order extensions of Einstein's equations. The required 4th-order extension of general relativity is given by adding quadratic curvature terms with coefficients that maintain a fixed ratio, as their magnitudes approach zero, with classical general relativity as a singular limit. If entangled particles are connected by a Planck-width ER bridge, as conjectured by Maldacena and Susskind, then a connection by a traversable Planck-scale wormhole, allowed in 4th-order gravity, describes such entanglement in the ontological interpretation. It is hypothesized that higher-derivative gravity can account for the nonlocal part of the quantum potential generally.     

Loop quantum modified gravity and its cosmological application

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.     

The search for quantum gravity effects I

In this contribution the search for effects from possible theories of quantum gravity is reviewed. In order to distinguish quantum gravity effects from standard effects, first the standard theory and the principles it is based on has to be described. We show that standard physics (the Maxwell equations, the Dirac equation, gravity as a metric theory) is completely based on the Einstein equivalence principle, EEP (for obtaining the Einstein equations, some more requirements are needed). As a consequence, all deviations from the EEP are related to new effects originating from quantum gravity. The variety and structure of these effects is described and the expected magnitude of the effects and a corresponding strategy for the search for these effects are discussed. We stress the advantages of space for performing experiments searching for quantum gravity effects. At the end we make some remarks concerning the daily-life applications of high-precision techniques. PACS 04.80.Cc; 03.30.+p; 06.20.-f; 04.60.-m     

Gravitational instantons

The path-integral approach to quantum field theory assigns special importance to finite action Euclidean solutions of classical field equations. In Yang-Mills gauge theories, the instanton solutions of classical field equations with self-dual field strength have given rise to a new, nonperturbative treatment of the quantum field theory and its vacuum state. Since gravitation is also a species of gauge theory, one might think that similar phenomena would occur in gravity. The authors recently sought and found a new self-dual solution to Euclidean gravity which plays a role parallel to that of the Yang-Mills instanton. Gravitational instantons now promise to yield new insights into the nature of quantum gravity.This essay received the second award from the Gravity Research Foundation for the year 1979-Ed.     

On Weyl invariance conditions in string theory coupled with two-dimensional gravity

The unified theory of string and two-dimensional quantum gravity is considered. We introduce nontrivial dynamics for the two-dimensional metric g_μν from the very beginning and calculate the path integral over the string coordinates and g_μν without taking into account the order of integrations. Throughout the paper we use two different kinds of gauges - the covariant one of the harmonic type and also the conformal gauge, where the original (D + 1)-dimensional sigma model with quantum gravity becomes the (D+2)-dimensional sigma model on the classical background of g_μν The general symmetries of the theory consist in the reparametrizations of the target space coordinates, in the conformal transformations of the metric and in the usual 2d diffeomorphisms. These symmetries do not disturb the structure of the background fields in the (D+2) -dimensional formulation. On the other hand the related arbitrariness of the renormalization does not affect the qualitative structure of the loop contributions to the Weyl anomaly. In the theory with quantum gravity the parameter a′ does not play as the parameter of the loop expansion. That is why the one-loop conditions of the Weyl invariance differs from the well known effective equations which arise in the standard approach when g_μν is not quantized simultaneously with the string coordinates. Therefore, despite the new conditions of the Weyl invariance for the background fields are different from the standard effective equations, our result does not contradict to the standard approach. The new one-loop conditions of the Weyl invariance are much more complicated and contain the higher derivatives in the dilaton sector.     

Quantum nature of cosmological bounces

Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a bounce has been realized under fairly general conditions, the central questions are how strongly quantum it behaves, what influence quantum effects can have on its appearance, and what quantum space-time beyond the bounce may look like. This, then, has to be taken into account for effective equations which describe the evolution properly and can be used for further phenomenological investigations. Here, we provide the first analysis with interacting matter with new effective equations valid for weak self-interactions or small masses. They differ from the free scalar equations by crucial terms and have an important influence on the bounce and the space-time around it. Especially the role of squeezed states, which have often been overlooked in this context, is highlighted. The presence of a bounce is proven for uncorrelated states, but as squeezing is a dynamical property and may change in time, further work is required for a general conclusion.     

Quantum Einstein’s equations and constraints algebra

In this paper we shall address this problem: Is quantum gravity constraints algebra closed and what are the quantum Einstein’s equations. We shall investigate this problem in the de-Broglie-Bohm quantum theory framework. It is shown that the constraint algebra is weakly closed and the quantum Einstein’s equations are derived.     

2 + 1 dimensional gravity as an exactly soluble system

By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels. Indeed, it is closely related to Yang-Mills theory with purely the Chern-Simons action, which recently has turned out to define a soluble quantum field theory. 2 + 1 dimensional gravity has a straightforward renormalized perturbation expansion, with vanishing beta function. 2 + 1 dimensional quantum gravity may provide a testing ground for understanding the role of classical singularities in quantum mechanics, may be related to the discrete series of Virasoro representations in 1 + 1 dimensions, and may be a useful tool in studying three-dimensional geometry.     

Nonperturbative solutions for canonical quantum gravity: An overview

In this paper we will make a survey of solutions to the Wheeler-De Witt equation which have been found up to now in Ashtekar's formulation for canonical quantum gravity. Roughly speaking they are classified into two categories, namely, Wilson-loop solutions and topological solutions. While the program of finding solutions which are composed of Wilson loops is still in its infancy, it is expected to be developed in the near future. Topological solutions are the only solutions at present which can be interpreted in terms of spacetime geometry. While the analysis made here is formal in the sense that we do not deal with rigorously regularized constraint equations, these topological solutions are expected to exist even in the fully regularized theory and they are considered to yield vacuum states of quantum gravity. We also make an attempt to review the spin network states as intuitively as possible. In particular, the explicit formulae for two kinds of measures on the space of spin network states are given.