What gravity waves are telling about quantum spacetime

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.

5 pages. v2: one paragraph, one note, and references added; v3: publication data added

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