Related papers: Multiscale spacetimes from first principles
By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized) causal dynamical triangulations and ordinary dynamical…
To explain the recently reported large-scale spatial variations of the fine structure constant $\alpha$, we apply some models of curvature-nonlinear multidimensional gravity. Under the reasonable assumption of slow changes of all quantities…
Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier.…
Getting signatures of quantum gravity is one of the topical lines of research in modern theoretical physics and cosmology. This short review faces this challenge under a novel perspective. Instead of separating quantum-gravity effects of a…
We compare the recently formulated multifractional spacetimes with field theories of quantum gravity based on the renormalization group (RG), such as asymptotic safety and Ho\v{r}ava--Lifshitz gravity. The change of spacetime dimensionality…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar patterns.…
We discuss the construction of cosmological models within the framework of Macroscopic Gravity (MG), which is a theory that models the effects of averaging the geometry of space-time on large scales. We find new exact spatially homogeneous…
Based on an extended time-space symmetry, a cylindrical model of gravitational geometrical dynamics with two time-like extra-dimensions leads to a microscopic geodesic description of the curved space-time. Due to interaction of a Higgs-like…
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 introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative…
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…
In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension $d$ at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is…
The spectral dimension has proven to be a very informative observable to understand the properties of quantum geometries in approaches to quantum gravity. In loop quantum gravity and its spin foam description, it has not been possible so…
We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four…
For a positive measure set of nonuniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given observable and consider the associated {\it…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…