Wide-angle effects on galaxy ellipticity correlations

We show an efficient way to compute wide-angle or all-sky statistics of galaxy intrinsic alignment in three-dimensional configuration space. For this purpose, we expand the two-point correlation function using a newly introduced spin-dependent tripolar spherical harmonic basis. Therefore, angular dependences on two line-of-sight (LOS) directions pointing each pair objects, which are degenerate with other conventional analysis under small-angle plane-parallel (PP) approximation, unambiguously decomposed. By means this, we, for first time, auto and cross correlations between ellipticities, number densities velocities galaxies, compare them PP-limit results. ellipticity-ellipticity density-ellipticity correlations, find more than $10\%$ deviation from results if opening angle LOS exceeds $30^\circ - 50^\circ$. It is also shown that even result strictly zero, non-vanishing obtained over various scales, arising purely curved-sky effects. Our indicate importance data not relying PP approximation order determine cosmological parameters precisely and/or new physics via ongoing forthcoming surveys.