Complete treatment of galaxy two-point statistics: Gravitational lensing effects and redshift-space distortions

摘要: We present a coherent theoretical framework for computing gravitational lensing effects and redshift-space distortions in an inhomogeneous universe investigate their impacts on galaxy two-point statistics. Adopt- ing the linearized Friedmann-Lemaˆ itre-Robertson-Walker metric, we derive generalized Sachs-Wolfe that include weak distortion, magnification, time delay effects, Sachs-Wolfe, integ rated respectively. Based this framework, first compute observed source fluctuations, separating them as two physically distinct origins: volume effect involves chang e of is always statistics, depends intrin sic properties populations. Then identify several terms are ignored standard method, ensemble average all combinations intrinsic fluctuations additional contributions from effects. This unified treatment two- point statistics clarifies relation gravitationa l to metric perturbations underlying matter fluctuation s. For near future dark energy surveys, analyze impact anisotropic structure. Thorough modeling would be not only necessary precision measurements upcoming but also provide further discriminatory power understanding physical mechanisms.