Projected bispectrum in spherical harmonics and its application to angulargalaxy catalogues

We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic microwave background and gravitational lensing studies. By expanding the 2D distribution of galaxies on the sky in spherical harmon ics, we show how the three-point function of the coefficients can be used i n principle to determine the bias parameter of the galaxy sample. If this c an be achieved, it would allow a lifting of the degeneracy between the bias and the matter density parameter of the Universe, which occurs in linear a nalysis of 3D galaxy catalogues. In previous papers, we have shown how a si milar analysis can be done in three dimensions, and we show here through an error analysis and by implementing the method on a simulated projected cat alogue that ongoing three-dimensional galaxy redshift surveys (even with al l the additional uncertainties introduced by partial sky coverage, redshift -space distortions and smaller numbers) will do far better than all-sky pro jected catalogues with similar selection function.