The observation of GW170817 in both gravitational and electromagnetic waves provides a number of unique tests of general relativity. One question we can answer with this event is: Do large-wavelength gravitational waves and short-frequency photons experience the same number of spacetime dimensions?
In models that include additional non-compact spacetime dimensions, as the gravitational waves propagate, they "leak" into the extra dimensions, leading to a reduction in the amplitude of the observed gravitational waves, and a commensurate systematic error in the inferred distance to the gravitational wave source. Electromagnetic waves would remain unaffected.
We compare the inferred distance to GW170817 from the observation of gravitational waves, dGWL, with the inferred distance to the electromagnetic counterpart NGC 4993, dEML. We constrain dGWL=(dEML/Mpc)γ with γ=1.01+0.04−0.05 (for the SHoES value of H0) or γ=0.99+0.03−0.05 (for the Planck value of H0), where all values are MAP and minimal 68% credible intervals.
These constraints imply that gravitational waves propagate in D=3+1 spacetime dimensions, as expected in general relativity. In particular, we find that D=4.02+0.07−0.10 (SHoES) and D=3.98+0.07−0.09 (Planck). Furthermore, we place limits on the screening scale for theories with D>4 spacetime dimensions, finding that the screening scale must be greater than ∼20 Mpc. We also place a lower limit on the lifetime of the graviton of t>4.50×10^8 yr.Pardo et al. 2018, "Limits on the number of spacetime dimensions from GW170817"
In many beyond the Standard Model theories, all particles and forces except gravity are confined to the 3+1 dimensions of General Relativity, but gravity can escape those dimensions to higher dimensions, which partially explains its relative weakness as a force. This result disfavors theories of that class.