# Information content of the angular multipoles of redshift-space galaxy bispectrum

Praful Gagrani, Lado Samushia

January, 2017

### Abstract

The redshift-space bispectrum (three point statistics) of galaxies depends on the expansion rate, the growth rate and the geometry of the Universe, and hence can be used to measure key cosmological parameters. In a homogeneous Universe, the bispectrum is a function of five variables and unlike its two point statistics counterpart – the power spectrum – which is a function of only two variables – is difficult to analyse unless the information is somehow reduced. The most commonly considered reduction schemes rely on computing angular integrals over possible orientations of the bispectrum triangle, thus reducing it to sets of function of only three variables describing the triangle shape. We use Fisher information formalism to study the information loss associated with this angular integration. Without any reduction, the bispectrum alone can deliver constraints on the growth rate parameter f that are better by a factor of 2.5 compared with the power spectrum, for a sample of luminous red galaxies expected from near future galaxy surveys at a redshift of z ∼ 0.65 if we consider all the wavenumbers up to k ≤ 0.2 h Mpc−1. At lower redshifts the improvement could be up to a factor of 3. We find that most of the information is in the azimuthal averages of the first three even multipoles. This suggests that the bispectrum of every configuration can be reduced to just three numbers (instead of a 2D function) without significant loss of cosmologically relevant information.