Propagation Of Gravitational Waves And Observational Constraints On Modified Gravity Models

Gravitational waves(GWs)are disturbances in the curvature of spacetime,generated by accelerated masses,that propagate as waves outward from their source.In gravitational-wave astronomy,observations of gravitational waves are used to infer data about the sources of gravitational waves.The important and unique properties of GWs allow them to carry information about astronomical phenomena heretofore never observed by humans.In this thesis,on the one hand,we study the polarization and propagation of a GW through the Friedmann-Lemaitre-Robertson-Walk universe.By considering the null geodesic deviations,we first provide a definition of the polarization of the GW in terms of the Weyl scalars with respect to a parallel-transported frame along the null geodesics,and then show explicitly that,due to different effects of the expansion of the universe on the two polarization modes,the so-called "+" and "×"modes,the polarization angle of the GW changes generically,when it is propagating through the curved background.By direct computations of the polarization angle,we show that different epochs,radiation-,matter-and ?-dominated,have different effects on the polarization.In particular,for a GW emitted by a binary system,we find explicitly the relation between the change of the polarization angle |??| and the redshift zs of the source in different epochs.In the ?CDM model,we find that the order of |??|?0F is typically O(10-3)to O(103),depending on the values of zs,where ?0 is the(comoving)time of the current universe,(?)with ?obs and Mc being,respectively,the time to coalescence in the observer's frame and the chirp mass of the binary system.On the other hand,in this thesis,we also investigate the observational constraints of gravitational waves on a modified gravity model,that is,regularized Einstein-Gauss-Bonnet(EGB)theory of gravity in four dimensions,which is a new attempt to include nontrivial contributions of Gauss-Bonnet term.We make a detailed analysis on possible constraints of the model parameters of the theory from recent cosmological observations,and some theoretical constraints as well.Our results show that the theory with vanishing bare cosmological constant,?0,is ruled out by the current observational value of wde,and the observations of GW170817 and GRB 170817A as well.For nonvanishing bare cosmological constant,instead,our results show that the current observation of the speed of GWs measured by GW 170817 and GRB 170817A would place a constraint on ?,a dimensionless parameter of the theory,as-7.78×10-16???3.33 ×10-15.