An Inventory of Bispectrum Estimators for Redshift Space Distortions
  In order to best improve constraints on cosmological parameters and on models
of modified gravity using current and future galaxy surveys it is necessary
maximally exploit the available data. As redshift-space distortions mean
statistical translation invariance is broken for galaxy observations, this will
require measurement of the monopole, quadrupole and hexadecapole of not just
the galaxy power spectrum, but also the galaxy bispectrum. A recent (2015)
paper by Scoccimarro demonstrated how the standard bispectrum estimator may be
expressed in terms of Fast Fourier Transforms (FFTs) to afford an extremely
efficient algorithm, allowing the bispectrum multipoles on all scales and
triangle shapes to be measured in comparable time to those of the power
spectrum. In this paper we present a suite of alternative proxies to measure
the three-point correlation multipoles. In particular, we describe a modal (or
plane wave) decomposition to capture the information in each multipole in a
series of basis coefficients, and also describe three compressed estimators
formed using the skew-spectrum, the line correlation function and the
integrated bispectrum, respectively. As well as each of the estimators offering
a different measurement channel, and thereby a robustness check, it is expected
that some (especially the modal estimator) will offer a vast data compression,
and so a much reduced covariance matrix. This compression may be vital to
reduce the computational load involved in extracting the available three-point
information.
