Anisotropies in luminosity distance

Anisotropies in the luminosity distance-redshift (d(L)-z) relation caused by the large-scale structure (LSS) of the universe are studied. We solve the Raychaudhuri equation in Friedmann-Robertson-Walker models, taking account of the LSS by the linear perturbation method. Numerical calculations to evaluate the amplitude of the anisotropies are carried out in flat models with the cosmological constant and in open models, employing the cold dark matter model and the COBE-normalization for the power spectrum of the density perturbation. The implications of our calculations for observation are discussed. These anisotropies in d(L) may cause uncertainties in determining cosmological parameters, e.g., the deceleration parameter q(0), via the magnitude-redshift relation. We found that the effects on the d(L)-z relation of the LSS are divided into three types: the peculiar velocity effect, gravitational lensing and the Sachs-Wolfe effect. We show that, for lower redshifts, the peculiar velocity effect is dominant, while around z greater than or similar to 0.5, the gravitational lensing is dominant, though the amplitude is rather small, affecting the estimate of q(0) by at most about 5%.