Gravitational wave signature of the fifth force for dark matter

Abstract

Abstract Testing the equivalence principle (EP) is of great importance for fundamental physics. Whether the EP is held for dark matter (DM) is still unclear. Motivated by the recent discoveries of gravitational waves (GWs) by ground based detectors, we study the possibility of testing EP of DM by GW experiments. We consider a binary composed of a black hole (BH) and a neutron star (NS) with respect to the galactic DM as the attractor. Possibly, long-range fifth-force other than gravity between DM and ordinary matter may lead to the EP violation for DM, we investigate the effect of fifth-force acted by DM on the GW waveform of the BH-NS binary. The presence of the fifth-force will lead to a phase correction in the GW waveform which may be detectable, but the phase correction depends chaotically on the initial condition. We calculate the probability of detection for different initial conditions. The probability depends on the time interval of integration, the EP-violating driving force and the initial eccentricity. We find for appropriate conditions the probability can reach to a considerable value, and even approach to 1 in some extremal cases. For example, for most BH-NS binaries formed in the field locating as far as the solar system to the galactic center, the fifth force with the Eötvös parameter η DM BH , NS ⩾ 0.01 will result in the probability of detection >0.6 if the interval of integral time is from f = 1 Hz to the final state when the NS is disrupted by the BH. These predictions may be tested by future GW observations.