Modal compression of the redshift-space galaxy bispectrum
  We extend the modal decomposition method, previously applied to compress the
information in the real-space bispectrum, to the anisotropic redshift-space
galaxy bispectrum. In the modal method approach, the bispectrum is expanded on
a basis of smooth functions of triangles and their orientations, such that a
set of modal expansion coefficients can capture the information in the
bispectrum. We assume a reference survey and compute Fisher forecasts for the
compressed modal bispectrum and two other basis decompositions of the
redshift-space bispectrum in the literature, one based on (single) spherical
harmonics and another based on tripolar spherical harmonics. In each case, we
compare the forecasted constraints from the compressed statistic with
forecasted constraints from the full, uncompressed bispectrum which includes
all triangles and orientations. Our main result is that all three compression
methods achieve good recovery of the full information content of the
bispectrum, but the modal decomposition approach achieves this the most
efficiently: only 14 (42) modal expansion coefficients are necessary to obtain
constraints that are within 10% (2%) of the full bispectrum result. The next
most efficient decomposition is the one based on tripolar spherical harmonics,
while the spherical harmonic multipoles are the least efficient.
