Related papers: The measure matters
We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations…
We explore the cosmological implications of a mechanism found in several approaches to quantum-gravity, whereby the spectral dimension of spacetime runs from the standard value of 4 in the infrared (IR) to a smaller value in the ultraviolet…
We re-examine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for…
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…
We revisit one of the earliest proposals for deformed dispersion relations in the light of recent results on dynamical dimensional reduction and production of cosmological fluctuations. Depending on the specification of the measure of…
Planck-scale dynamical dimensional reduction is attracting more and more interest in the quantum-gravity literature since it seems to be a model independent effect. However different studies base their results on different concepts of…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
There is a growing evidence that due to quantum gravity effects the effective spacetime dimensionality might change in the UV. In this letter we investigate this hypothesis by using quantum fields to derive the UV behaviour of the static,…
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…
We consider gauge invariant cosmological perturbations in UV-modified, z=3 Horava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. In order to…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
We show that there exists a divergent correlation length in 2d quantum gravity for the matter fields close to the critical point provided one uses the invariant geodesic distance as the measure of distance. The corresponding…
We conduct numerical simulations of a model of four dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume the model contains a…
In this manuscript, a conformally invariant theory of gravitation in the context of metric measure space is studied. The proposed action is invariant under both diffeomorphism and conformal transformations. Using the variational method, a…
We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z=3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short…
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here,…
I formulate several statements demonstrating that the local metric redefinition can be used to reduce the UV divergences present in the quantum action for the Einstein gravity in $d=4$ dimensions. In its most general form, the proposal is…
This note is based on F. Burghart's master thesis at Stuttgart university from July 2018, supervised by Prof. Freiberg. We review the Einstein relation, which connects the Hausdorff, local walk and spectral dimensions on a space, in the…