Spherically symmetric solutions of the λ\lambda-R model

We derive spherically symmetric solutions of the classical \lambda-R model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. Starting from a 3 + 1 decomposition of the four-metric in a general spherically symmetric ansatz, we perform a phase space analysis of the reduced model. We show that its constraint algebra is consistent with that of the full \lambda-R model, and also yields a constant mean curvature or maximal slicing condition as a tertiary constraint. Although the solutions contain the standard Schwarzschild geometry for the general relativistic value \lambda = 1 or for vanishing mean extrinsic curvature K, they are in general non-static, incompatible with asymptotic flatness and parametrized not only by a conserved mass. We show by explicit computation that the four-dimensional Ricci scalar of the solutions is in general time-dependent and nonvanishing.Comment: 30 pages, no figure

Locally Causal Dynamical Triangulations in Two Dimensions

We analyze the universal properties of a new two-dimensional quantum gravity model defined in terms of Locally Causal Dynamical Triangulations (LCDT). Measuring the Hausdorff and spectral dimensions of the dynamical geometrical ensemble, we find numerical evidence that the continuum limit of the model lies in a new universality class of two-dimensional quantum gravity theories, inequivalent to both Euclidean and Causal Dynamical Triangulations

Simulating CDT quantum gravity

We provide a hands-on introduction to Monte Carlo simulations in nonperturbative lattice quantum gravity, formulated in terms of Causal Dynamical Triangulations (CDT). We describe explicitly the implementation of Monte Carlo moves and the associated detailed-balance equations in two and three spacetime dimensions. We discuss how to optimize data storage and retrieval, which are nontrivial due to the dynamical nature of the lattices, and how to reconstruct the full geometry from selected stored data. Various aspects of the simulation, including tuning, thermalization and the measurement of observables are also treated. An associated open-source C++ implementation code is freely available online

Putting a cap on causality violations in CDT

The formalism of causal dynamical triangulations (CDT) provides us with a non-perturbatively defined model of quantum gravity, where the sum over histories includes only causal space-time histories. Path integrals of CDT and their continuum limits have been studied in two, three and four dimensions. Here we investigate a generalization of the two-dimensional CDT model, where the causality constraint is partially lifted by introducing weighted branching points, and demonstrate that the system can be solved analytically in the genus-zero sector.Comment: 17 pages, 4 figure

CDT and cosmology

In the approach of Causal Dynamical Triangulations (CDT), quantum gravity is obtained as a scaling limit of a non-perturbative path integral over space-times whose causal structure plays a crucial role in the construction. After some general considerations about the relation between quantum gravity and cosmology, we examine which aspects of CDT are potentially interesting from a cosmological point of view, focussing on the emergence of a de Sitter universe in CDT quantum gravity.Comment: 14 pages, invited review for a special issue of Compte Rendus Physiqu

A String Field Theory based on Causal Dynamical Triangulations

We formulate the string field theory in zero-dimensional target space corresponding to the two-dimensional quantum gravity theory defined through Causal Dynamical Triangulations. This third quantization of the quantum gravity theory allows us in principle to calculate the transition amplitudes of processes in which the topology of space changes in time, and to include non-trivial topologies of space-time. We formulate the corresponding Dyson-Schwinger equations and illustrate how they can be solved iteratively.Comment: 29 pages, 4 figure

Group-theoretical and BRS quantization of constrained systems

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Causal dynamical triangulations and the search for a theory of quantum gravity

Causal dynamical triangulations provide a nonperturbative regularization of a theory of quantum gravity. We describe how it connects to the asymptotic safety program and to the Hořava–Lifshitz gravity theory and present the most recent results from computer simulations