O., & Woodard, R

On August 17, 2017 the LIGO interferometers detected the gravitational wave (GW) signal (GW170817) from the coalescence of binary neutron stars. This signal was also simultaneously seen throughout the electromagnetic (EM) spectrum from radio waves to gamma-rays. We point out that this simultaneous detection of GW and EM signals rules out a class of modified gravity theories, termed ``dark matter emulators,'' which dispense with the need for dark matter by making ordinary matter couple to a different metric from that of GW. We discuss other kinds of modified gravity theories which dispense with the need for dark matter and are still viable. This simultaneous observation also provides the first observational test of Einstein's Weak Equivalence Principle (WEP) between gravitons and photons. We estimate the Shapiro time delay due to the gravitational potential of the total dark matter distribution along the line of sight (complementary to the calculation in arXiv:1710.05834) to be about 400 days. Using this estimate for the Shapiro delay and from the time difference of 1.7 seconds between the GW signal and gamma-rays, we can constrain violations of WEP using the parameterized post-Newtonian (PPN) parameter $\gamma$, and is given by $|\gamma_{\rm {GW}}-\gamma_{\rm{EM}}|<9.8 \times 10^{-8}$.