Correlations of Cosmic Tidal Fields

Abstract

We study correlations amongst tidal fields originated by the large-scale distribution of matter in the Universe. The two-point tidal correlation is described as a rank-4 tensor, whose elements can be written in terms of four fundamental scalar functions ranging, with respect the spatial separation, from purely transversal to purely longitudinal correlations. Tidal fields, both on galaxy and cluster scales, reveal to be correlated over distances larger than the mass-density correlation lenght, though traceless tidal fields show anti-correlation between diagonal terms along orthogonal directions. The cross-correlation between mass and tidal field is also analyzed. These results are relevant for galaxy formation and the interpretation of large-scale weak lensing phenomena.