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