The three-dimensional distribution of astronomical objects observed in redshift space significantly differs from the true distribution, since the distance to each object cannot be determined by its redshift z only; for z ≪ 1 the peculiar velocity field contaminates the true recession velocity of the Hubble flow, while the true distance for objects with z ≳ 1 sensitively depends on the (unknown and thus assumed) cosmological parameters. This hampers the effort to understand the true distribution of the large-scale structure of the universe. In addition, all cosmological observations are carried out on a light-cone, the null hypersurface of an observer at z = 0. This implies that their intrinsic properties and clustering statistics should change even within the survey volume. Therefore, a proper comparison taking account of the light-cone effect is important to extract any cosmological information from redshift catalogues, especially for z ≳ 1. We present recent theoretical developments on the two effects - the cosmological light-cone effect and the cosmological redshift-space distortion - that should play key roles in observational cosmology in the 21st century.
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