What gravity waves are telling about quantum spacetime

TL;DR

This paper examines how quantum gravity-inspired modifications to gravitational wave dispersion relations could be constrained by GW150914 data, finding current bounds are weak and exploring phenomenological models compatible with observations.

Contribution

It analyzes the constraints on quantum gravity effects from gravitational wave data and introduces a phenomenological dispersion relation compatible with current observations.

Findings

Bounds on quantum gravity scale are weaker than expected.

A specific dispersion relation can fit data with a quantum gravity scale above 10 TeV.

Multiscale spacetimes are compatible with the phenomenological model.

Abstract

We discuss various modified dispersion relations motivated by quantum gravity which might affect the propagation of the recently observed gravitational-wave signal of the event GW150914. We find that the bounds set by the data on the characteristic quantum-gravity mass scale $M$ are too weak to constrain these scenarios and, in general, much weaker than the expected $M> 10^4\,\text{eV}$ for a correction to the dispersion relation linear in $1/M$. We illustrate this issue by giving lower bounds on $M$, plus an upper bound coming from constraints on the size of a quantum ergosphere. We also show that a phenomenological dispersion relation $\omega^2 = k^2(1+\alpha k^n/M^n)$ is compatible with observations and, at the same time, has a phenomenologically viable mass $M>10\,\text{TeV}$ only in the quite restrictive range $0<n<0.68$. Remarkably, this is the domain of multiscale spacetimes but not of known quantum-gravity models.