Mixing Bispectrum Multipoles Under Geometric Distortions

TL;DR

This paper derives analytic formulas for how geometric distortions affect the bispectrum multipoles in cosmology, enabling simplified analysis of galaxy survey data and improving measurement accuracy.

Contribution

It provides explicit linear approximation formulas for bispectrum multipole mixing coefficients under Alcock-Paczynski distortions, enhancing analysis efficiency.

Findings

Linear approximation is highly accurate for power spectrum multipoles.

Approximate formulas work well for bispectrum monopole.

Inaccuracies arise at sub-percent level for bispectrum quadrupole and fail for hexadecapole.

Abstract

We derive general expressions for how the Alcock-Paczynski distortions affect the power spectrum and the bispectrum of cosmological fields. We compute explicit formulas for the mixing coefficients of bispectrum multipoles in the linear approximation. The leading-order effect for the bispectrum is the uniform dilation of all three wavevectors. The mixing coefficients depend on the shape of the bispectrum triplet. Our results for the bispectrum multipoles are framed in terms of the "natural" basis of the lengths of three wavevectors but can be easily generalized for other bases and reduction schemes. Our validation tests confirm that the linear approximation is extremely accurate for all power spectrum multipoles. The linear approximation is accurate for the bispectrum monopole but results in sub-percent level inaccuracies for the bispectrum quadrupole and fails for the bispectrum hexadecapole. Our results can be used to simplify the analysis of the bispectrum from galaxy surveys, especially the measurement of the Baryon Acoustic Oscillation peak position. They can be used to replace numeric schemes with exact analytic formulae.