Related papers: Quantum Gravity via Manifold Positivity
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…
One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…
Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic…
We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
The main obstacle in attempts to construct a consistent quantum gravity is the absence of independent flat time. This can in principle be cured by going out to higher dimensions. The modern paradigm assumes that the fundamental theory of…
We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the…
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…
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional…
The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…
If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches…
In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are…
We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…
Combinatorial quantum gravity is governed by a discrete Einstein-Hilbert action formulated on an ensemble of random graphs. There is strong evidence for a second-order quantum phase transition separating a random phase at strong coupling…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…