Shortcut in codimension-2 brane cosmology in light of GW170817

In this paper, our universe is regarded as a codimension-2 brane embedded in a noncompact six dimensional Anti-de Sitter (AdS) spacetime. We derive the gravitational horizon radius on the brane under the low energy approximation, which reflects how the extra dimensions cause the shortcut effect of gravitational waves (GWs). We also study the time delay between a GW signal and an electromagnetic (EM) wave signal in the low-redshift limit by combining with the joint observations of GW170817 and GRB 170817A, which gives an upper limit to the AdS(6) radius as l(2) ? 3.84 Mpc(2). For a high-redshift source, the time delay is converted into the discrepancy between the source redshift derived from the GW signal and the one derived from the EM counterpart. It is found that if one expects to detect the EM counterpart of a high-redshift GW event within a reasonable observation time, it requires a stronger constraint on the AdS6 radius. Our research shows that the AdS6 radius should satisfy l(2) ? 0.02 Mpc(2) for the DECIGO and BBO.