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The recent detections of the gravitational wave (GW) event GW170817 and itselectromagnetic counterpart GRB 170817A produced by a binary neutron star (NS)merger is a new milestone of multimessenger astronomy. The time intervalbetween these two signals has attracted widespread attention from physicists.In the braneworld scenario, GWs could propagate through the bulk whileelectromagnetic waves (EMWs) are bounded on the brane, i.e., our Universe.Therefore, the trajectories of GWs and EMWs may follow different pathes. If GWsand EMWs are originated simultaneously from the same source on the brane, theyare expected to arrive at the observer successively. Consequently, the timedelay between GW170817 and GRB 170817A may carry the information of the extradimension. In this paper, we try to investigate the phenomenon in the contextof a five-dimensional dS ($\text{dS}_5$) spacetime. We first study two specialUniverse models, i.e., de Sitter and Einstein-de Sitter models, and calculatethe gravitation horizon radius in each case. For the real Universe, we thenconsider the $\Lambda$CDM model. Our results show that for the de Sitter modelof the Universe, the $\text{dS}_5$ radius could not contribute to the timedelay. With the data of the observation, we constrain the $\text{dS}_5$ radiusto $\ell\gtrsim7.5\times10^{2}\,\text{Tpc}$ for the Einstein-de Sitter modeland $\ell\gtrsim2.4\times10^{3}\,\text{Tpc}$ for the $\Lambda$CDM model. Afterconsidering the uncertainty in the source redshift and the time-lags given bydifferent astrophysical processes of the binary NS merger, we find that ourconstraints are not sensitive to the redshift in the range of (0.005, 0.01) andthe time-lag in the range of (-100s, 1.734s).

Constraint on the radius of five-dimensional dS spacetime with GW170817 and GRB 170817A