Limits on the number of spacetime dimensions from GW170817

Kris Pardo; Maya Fishbach; Daniel E. Holz; David N. Spergel

doi:10.1088/1475-7516/2018/07/048

paper

Limits on the number of spacetime dimensions from GW170817

arXiv:1801.08160 · doi:10.1088/1475-7516/2018/07/048

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, $d_{L}^{GW}$ , with the inferred distance to the electromagnetic counterpart NGC 4993, $d_{L}^{EM}$ . We constrain $d_{L}^{GW} = (d_{L}^{EM} / Mpc)^{γ}$ with $γ = 1.0 1_{- 0.05}^{+ 0.04}$ (for the SHoES value of $H_{0}$ ) or $γ = 0.9 9_{- 0.05}^{+ 0.03}$ (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 $D = 4.0 2_{- 0.10}^{+ 0.07}$ (SHoES) and $D = 3.9 8_{- 0.09}^{+ 0.07}$ (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 $t > 4.50 \times 1 0^{8}$ yr.

v3: fixed typo in abstract; v2: text changes + new figure, accepted for publication in JCAP

Limits on the number of spacetime dimensions from GW170817

Abstract

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