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We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
Two-dimensional quantum gravity has led to numerous curious results since it was developed in the 1980s. Following the method of the original works, we derive the effective action for the simplest modifications of the theory, when the…
Quantum gravity is known to be mostly a kind of metaphysical speculation. In this brief essay, we try to argue that, although still extremely difficult to reach, observational signatures can in fact be expected. The early universe is an…
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…
We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the…
The idea that quantum gravity can be realized at the TeV scale is extremely attractive to theorists and experimentalists alike. This proposal leads to extra spacial dimensions large compared to the electroweak scale. Here we give a very…
We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within…
Euclidean quantum gravity might be defined by stochastic quantisation that is governed by a higher order Langevin equation rather than a first order stochastic equation. In a transitory phase where the Lorentz time cannot be defined, the…
In this short paper, we propose a new quantum effect that naturally emerges from describing the quantum particle as a classical fluid. Following the hydrodynamical formulation of quantum mechanics for a particle in a finite convex region,…
General two-dimensional pure dilaton-gravity can be discussed in a unitary way by introducing suitable field redefinitions. The new fields are directly related to the original spacetime geometry and in the canonical picture they generalize…
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…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of…
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…
Quantum theory of a test field on a quantum cosmological spacetime may be viewed as a theory of the test field on an emergent classical background. In such a case, the resulting dressed metric for the field propagation is a function of the…
We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Besides the String Theory context, the quantum General Relativity can be studied by the use of constrained topological field theories. In the celebrated Plebanski formalism, the constraints connecting topological field theories and gravity…
An earlier proposed theory with linear-gonihedhic action for quantum gravity is reviewed. One can consider this theory as a "square root" of classical gravity with a new fundamental constant of dimension one. We demonstrate also, that the…
Within the framework of the previously proposed formulation of the quantum theory of gravity in terms of world histories, it was suggested that the universe has its own mass. This quantity is analogous to the mass of a particle in…