Projected bispectrum in spherical harmonics and its application to angular galaxy catalogues

Abstract

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 harmonics, we show how the 3-point function of the coefficients can be used in principle to determine the bias parameter of the galaxy sample. If this can 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 analysis of 3D galaxy catalogues. In previous papers we have shown how a similar analysis can be done in three dimensions, and we show here, through an error analysis and by implementing the method on a simulated projected catalogue, that ongoing three-dimensional galaxy redshift surveys (even with all the additional uncertainties introduced by partial sky coverage, redshift-space distortions and smaller numbers) will do far better than all-sky projected catalogues with similar selection function.

Minor changes to match the accepted version (MNRAS, 15 pages, 4 figures)

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• Stochasticity of Bias and Nonlocality of Galaxy Formation: Linear Scales
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• A Practical Computational Method for the Anisotropic Redshift-Space 3-Point Correlation Function
• Combining weak lensing tomography and spectroscopic redshift surveys
• Non-Gaussianity from Large-Scale Structure Surveys
• Relativistic wide-angle galaxy bispectrum on the light-cone
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• Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues
• Isotropic N-Point Basis Functions and Their Properties
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• Tidal alignments as a contaminant of the galaxy bispectrum
• Disentangling interacting dark energy cosmologies with the three-point correlation function
• Crawling the Cosmic Network: Exploring the Morphology of Structure in the Galaxy Distribution
• A numerical study of the effects of primordial non-Gaussianities on weak lensing statistics
• The VIMOS Public Extragalactic Redshift Survey (VIPERS). Exploring the dependence of the three-point correlation function on stellar mass and luminosity at 0.5<z<1.1
• Projected Three-Point Correlation Functions and Galaxy Bias
• The gravitational and lensing-ISW bispectrum of 21cm radiation
• Non-Gaussianity vs. non-linearity of cosmological perturbations
• Hydrodynamical chemistry simulations of the SZ effect and the impacts from primordial non-Gaussianities
• Detection of nonrandom patterns in cosmological gravitational clustering
• Projected two- and three-point statistics: Forecasts and mitigation of non-linear RSDs