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, $d_L^\mathrm{ GW}$, with the inferred distance to the electromagnetic counterpart NGC 4993, $d_L^\mathrm{ EM}$. We constrain $d_L^\mathrm{ GW} = (d_L^\mathrm{ EM}/\mathrm{ Mpc})^\mathrm{ \gamma}$ with $\gamma = 1.01^{ +0.04}_{ -0.05}$ (for the SHoES value of $H_0$) or $\gamma = 0.99^{ +0.03}_{ -0.05}$ (for the Planck value of $H_0$), 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 $\sim 20$ Mpc. We also place a lower limit on the lifetime of the graviton of $t > 4.50 \times 10^8$ yr.
Categories: gr-qc astro-ph.CO