Information Content of the Angular Multipoles of Redshift-Space Galaxy Bispectrum

TL;DR

This paper investigates the information content of the redshift-space galaxy bispectrum's angular multipoles, showing that most cosmological information can be captured with just three numbers per configuration, enhancing parameter constraints.

Contribution

The study demonstrates that reducing the bispectrum to three angular multipole components retains most cosmological information, improving parameter constraints over traditional methods.

Findings

Bispectrum provides 2.5 to 3 times better constraints on growth rate than power spectrum.

Most information is contained in the first three even multipoles.

Reducing bispectrum to three numbers per configuration preserves key cosmological information.

Abstract

The redshift-space bispectrum (three point statistics) of galaxies depends on the expansion rate, the growth rate, and 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 to the power spectrum, for a sample of luminous red galaxies expected from near future galaxy surveys at a redshift of $z\sim0.65$. 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.