Limits on the number of spacetime dimensions from GW170817

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, d_L ^GW, with the inferred distance to the electromagnetic counterpart NGC 4993, d_L ^EM. We constrain d_L ^GW = (d_L ^EM/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 × 10⁸ yr.