Related papers: Reconstructing the Universe
The aim of the causal dynamical triangulations approach is to define nonperturbatively a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. My aim in this paper is to give a concise yet…
We attempt to find new symmetries in the space-time structure, leading to a modified gravitation at large length scales, which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified…
Suppose the usual description of spacetime as a 4-dimensional manifold with a Lorentzian metric breaks down at Planck energies. Can we still construct sensible theoretical models of the universe? Are they testable? Do they lead to a…
One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it…
Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues.…
The model of Lorentzian three-dimensional dynamical triangulations provides a non-perturbative definition of three-dimensional quantum gravity. The theory has two phases: a weak-coupling phase with quantum fluctuations around a…
We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of…
These Lecture Notes provide an elementary introduction to the quantization of two-dimensional quantum gravity. Nothing beyond undergratuate physics and mathematic is required. Explicit formulas for the partition functions for universes with…
Quantum-gravity renders the space-time dimension to depend on the size of region; it monotonically increases with the size of region and asymptotically approaches four for large distances. This effect was discovered in numerical simulations…
The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of…
Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the…
In this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
Curvature is a key notion in General Relativity, characterizing the local physical properties of spacetime. By contrast, the concept of curvature has received scant attention in nonperturbative quantum gravity. One may even wonder whether…
Developments in theoretical cosmology in the recent decades show a close connection with particle physics, quantum gravity and unified theories. Answers or hints to many fundamental questions in cosmology like the homogeneity and isotropy…
In the time-space symmetric version of dynamical triangulation, a non-perturbative version of quantum Einstein gravity, numerical simulations without matter have shown two phases, with spacetimes that are either crumpled or elongated like…