Constraint on the radius of five-dimensional dS spacetime with GW170817 and GRB 170817A. (arXiv:2001.06581v1 [gr-qc])

Constraint on the radius of five-dimensional dS spacetime with GW170817 and GRB 170817A. (arXiv:2001.06581v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Lin_Z/0/1/0/all/0/1">Zi-Chao Lin</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Yu_H/0/1/0/all/0/1">Hao Yu</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Liu_Y/0/1/0/all/0/1">Yu-Xiao Liu</a>

The recent detections of the gravitational wave (GW) event GW170817 and its
electromagnetic counterpart GRB 170817A produced by a binary neutron star (NS)
merger is a new milestone of multi-messenger astronomy. The time interval
between these two signals has attracted widespread attention from physicists.
In the braneworld scenario, GWs could propagate through the bulk while
electromagnetic waves (EMWs) are bounded on the brane, i.e., our Universe.
Therefore, the trajectories of GWs and EMWs may follow different pathes. If GWs
and EMWs are originated simultaneously from the same source on the brane, they
are expected to arrive at the observer successively. Consequently, the time
delay between GW170817 and GRB 170817A may carry the information of the extra
dimension. In this paper, we try to investigate the phenomenon in the context
of a five-dimensional dS ($text{dS}_5$) spacetime. We assume two special
models for our Universe, i.e., the de Sitter model and the Einstein-de Sitter
model, and compare the gravitation horizon radius and photon horizon radius in
each case. Our results show that the $text{dS}_5$ radius will contribute to
the time delay in the latter case. With the data of the observation, we
constrain the $text{dS}_5$ radius to $ellgtrsim7.5times10^{2},text{Tpc}$.
After considering the uncertainty in the source redshift and the time-lags
given by different astrophysical processes of the binary NS merger, we find
that our constraint is not sensitive to the redshift in the range of (0.005,
0.01) and the time-lag in the range of (-100 s, 1.734 s).

The recent detections of the gravitational wave (GW) event GW170817 and its
electromagnetic counterpart GRB 170817A produced by a binary neutron star (NS)
merger is a new milestone of multi-messenger astronomy. The time interval
between these two signals has attracted widespread attention from physicists.
In the braneworld scenario, GWs could propagate through the bulk while
electromagnetic waves (EMWs) are bounded on the brane, i.e., our Universe.
Therefore, the trajectories of GWs and EMWs may follow different pathes. If GWs
and EMWs are originated simultaneously from the same source on the brane, they
are expected to arrive at the observer successively. Consequently, the time
delay between GW170817 and GRB 170817A may carry the information of the extra
dimension. In this paper, we try to investigate the phenomenon in the context
of a five-dimensional dS ($text{dS}_5$) spacetime. We assume two special
models for our Universe, i.e., the de Sitter model and the Einstein-de Sitter
model, and compare the gravitation horizon radius and photon horizon radius in
each case. Our results show that the $text{dS}_5$ radius will contribute to
the time delay in the latter case. With the data of the observation, we
constrain the $text{dS}_5$ radius to $ellgtrsim7.5times10^{2},text{Tpc}$.
After considering the uncertainty in the source redshift and the time-lags
given by different astrophysical processes of the binary NS merger, we find
that our constraint is not sensitive to the redshift in the range of (0.005,
0.01) and the time-lag in the range of (-100 s, 1.734 s).

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