  On 17 August 2017, a gravitational wave event (GW170817) and an associated
short gamma-ray burst (GRB 170817A) from a binary neutron star merger had been
detected. The followup optical/infrared observations also identified the
macronova/kilonova emission (AT2017gfo). In this work we discuss some
implications of the remarkable GW170817/GRB 170817A/AT2017gfo association. We
show that the $\sim 1.7$s time delay between the gravitational wave (GW) and
GRB signals imposes very tight constraint on the superluminal movement of
gravitational waves (i.e., the relative departure of GW velocity from the speed
of light is $\leq 4.3\times 10^{-16}$) or the possible violation of weak
equivalence principle (i.e., the difference of the gamma-ray and GW
trajectories in the gravitational field of the galaxy and the local universe
should be within a factor of $\sim 3.4\times 10^{-9}$). The so-called Dark
Matter Emulators and a class of contender models for cosmic acceleration
("Covariant Galileon") are ruled out, too. The successful identification of
Lanthanide elements in the macronova/kilonova spectrum also excludes the
possibility that the progenitors of GRB 170817A are a binary strange star
system. The high neutron star merger rate (inferred from both the local sGRB
data and the gravitational wave data) together with the significant ejected
mass strongly suggest that such mergers are the prime sites of heavy r-process
nucleosynthesis.

High Energy Astrophysical Phenomena;General Relativity and Quantum Cosmology