Optimal computation of anisotropic galaxy three point correlation function multipoles using 2DFFTLOG formalism. (English) Zbl 1485.83185
Summary: We study two key issues militating against the use of the anisotropic three-point correlation function (3PCF) for cosmological parameter inference: difficulties with its computational estimation and high-dimensionality. We show how high-dimensionality may be reduced significantly by multipole decompositions of all angular dependence. This allows deriving the full expression for the multipole moments of the anisotropic 3PCF and its covariance matrix in a basis where the dimensionality reduces from nine to two at each multipole in the plane-parallel limit. We use 2D FFTLog formalism to show how the multipole moments with double momentum integrals over the product of bispectrum and two highly oscillating spherical Bessel functions and its covariance with double momentum integrals over the product of three galaxy power spectra and a combination of four highly oscillating spherical Bessel functions may be computed optimally.
MSC:
| 83F05 | Relativistic cosmology |
| 81V35 | Nuclear physics |
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
| 76Q05 | Hydro- and aero-acoustics |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 81V60 | Mono-, di- and multipole moments (EM and other), gyromagnetic relations |
| 62J10 | Analysis of variance and covariance (ANOVA) |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
Keywords:
baryon acoustic oscillations; cosmological parameters from LSS; power spectrum; redshift surveysReferences:
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