Related papers: Multiscale spacetimes from first principles

Planck-scale physics challenges the classical smooth-spacetime picture by introducing quantum fluctuations that imply a nontrivial spacetime microstructure. We present a framework that encodes these fluctuations by promoting local scale…

Our study addresses the inference of jumps (i.e. sets of discontinuities) within multivariate signals from noisy observations in the non-parametric regression setting. Departing from standard analytical approaches, we propose a new…

The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional arguments it is demonstrated that any…

We explore the phenomenological implications of generalizing measures to a multidimensional multiverse. We consider a simple model in which the vacua are nucleated from a $D$-dimensional parent spacetime through dynamical compactification…

We initiate the study of Horava-Lifshitz models of gravity in the framework of spectral geometry. As the first step, we calculate the dimension of space-time. It is shown, that for the natural choice of a Dirac operator (or rather…

Spacetimes in general relativity can be uniquely decomposed into a set of multipole moments. Given the usefulness of moments in the categorization of radiation patterns, tidal deformations, and other phenomena associated with compact…

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…

We consider globally hyperbolic flat spacetimes in 2+1 and 3+1 dimensions, in which a uniform light signal is emitted on the $r$-level surface of the cosmological time for $r\to 0$. We show that the frequency of this signal, as perceived by…

Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…

A possibility to represent the standard model of fundamental particles covariant derivatives by means of approximate generalized fractional Riemann-Liouville derivatives of multifractal time and space model is shown.

Studies of the effective regime of loop quantum gravity (LQG) revealed that, in the limit of Planckian curvature scales, spacetime may undergo a transition from the Lorentzian to Euclidean signature. This effect is a consequence of quantum…

In this short note, we show that, in any given metric space, every Lipschitz open-map image of every subset of a given metric space whose boundary is Hausdorff-null is Hausdorff-measurable with respect to the same dimension. The main…

We study the possibility to obtain cosmological late-time acceleration from a geometry changing with the scale, in particular, in the so-called multifractional theories with $q$-derivatives and with weighted derivatives. In the theory with…

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…

We prove bounds for the almost sure value of the Hausdorff dimension of the limsup set of a sequence of balls in $\mathbf{R}^d$ whose centres are independent, identically distributed random variables. The formulas obtained involve the rate…

We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from…

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…

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 construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…

We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…