The Study Of The Localization And Probe For The Dark Matter Environment Of Gravitational Wave Sources,and The Test Of Brans-Dicke Theory

Since the frst observation of gravitational waves（GWs）by LIGO（Laser Interferometer Gravitational-wave Observatory）and Virgo collaborations in 2015,a new era of exploring gravity and the universe was ushered.The detections of GWs not only opened a new window to understand the properties of gravity,but also made it possible to test general relativity and modifed gravity in strong feld and nonlinear regimes.Thousands of cycles of GW signals radiated from large mass ratio inspirals can be ob-served by future space-based GW detectors.More importantly,these waveforms not only carry rich information about the GW sources,but also encode the information about the en-vironment and underlying gravity theories.Therefore,the observations of GWs from large mass ratio inspirals can be used to explore the properties of dark matter（DM）and gravity in strong feld and nonlinear regions.To achieve the above scientifc goals of proposed space-based GW detectors,frstly we need to accurately locate the position of the GW source.It is difcult for the space-based GW detector satellites to maintain a fxed distance from each other during the operation,so the laser frequency noise cannot be cancelled out,so we need to consider time-delay interferometry（TDI）.Taking the frst-generation TDI method into account to eliminate the laser frequency noise and employing the Fisher information matrix（FIM）,we study the efects of these factors,including the time-changing orientation of the detector plane,arm length,period,and noise curve,on the localization of monochromatic GW sources.We also calculate the angular resolution with LISA（Laser Interferometer Space Antenna）,Taiji,Tianqin,and their network at diferent GW frequency.We found the angular resolution is almost the same with or without TDI combination.But the TDI technology must be considered in the actual signal processing.For the intermediate mass ratio inspiral（IMRI）systems in the DM environments,based on the Keplerian orbit,we use the osculating orbit method to calculate the orbital evolution of the system.We found that the main efect of DM occurs in the region p（?）10⁵R_s（R_s is the Schwarzschild radius of the black hole）,and the gravitational efect of DM causes retrograde precession of the orbit.The efects of accretion,dynamical friction and radiation reaction of GW cause a faster decay of the orbit.Besides,the efects of accretion and dynamical friction increase the eccentricity,the efect of radiation reaction of GW decreases the eccentricity.The combined efect of these factors causes the eccentricity of the orbit to slowly increase and then rapidly decay.The mass growth caused by the small object accretion shortens the merger time of the system,and increases the amplitude and frequency of the GW.In addition,we calculat the signal-to-noise ratio（SNR）and the mismatch for IMRI with and without DM environments,and found that the signal can be detected by future space-based GW detectors,we also employ the FIM to estimate the dark matter density parameter for circular orbit.In Brans-Dicke（BD）theory,the presence of the scalar feld excites the breathing po-larization of GWs,resulting in monopole and dipole radiations.The extra radiation channel makes the orbital evolutions and GW waveforms of I/EMRIs diferent from those in GR.Based on the osculating orbit method,we calculate the orbit evolution of I/EMRIs in GR and BD theories.With the help of accurate orbit motion,we calculate the GW waveform tem-plates including monopolar and dipolar radiation contributions for eccentric orbits in BD theory.Taking the LISA detector as an example,we constrain the BD coupling parame-te rw₀.Through two-year observations of GW from I/EMRIs,we use the mismatch of GW waveform templates to distinguish the BD theory from GR,and obtain the most stringent pre-constraint on the BD coupling parameter w₀>10⁶.