Lorentz violations in multifractal spacetimes

TL;DR

Using gravitational wave observations, the paper establishes strong bounds on the energy scale where multifractal spacetime effects and Lorentz violations become significant, significantly improving previous constraints and exploring implications of discrete spacetime structures.

Contribution

The paper provides the first bounds on the energy scale of multifractal spacetime effects using gravitational wave data, showing these effects occur above 10^{14} GeV, much lower than previous limits.

Findings

Multifractal effects become apparent above 10^{14} GeV.

Logarithmic oscillations do not significantly alter bounds unless finely tuned.

Bounds are much stronger than those from gamma-ray burst observations.

Abstract

Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with $q$-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is $E_*>10^{14}\,{\rm GeV}$ (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value $1/2$. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which $E_*> 10^{17}\,{\rm GeV}$ or greater.