Limits on the number of spacetime dimensions from GW170817

TL;DR

This paper uses GW170817 observations to test if gravitational waves and photons experience the same number of spacetime dimensions, constraining the existence of extra dimensions and confirming general relativity.

Contribution

It provides the first constraints on the number of spacetime dimensions using gravitational wave and electromagnetic observations from GW170817.

Findings

Gravitational waves propagate in 3+1 dimensions, consistent with general relativity.

Limits on extra dimensions imply the screening scale exceeds ~20 Mpc.

Lower bound on graviton lifetime is 4.5 x 10^8 years.

Abstract

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.