### Abstract

Redshift-space distortions in galaxy surveys happen along the radial direction, breaking statistical translation invariance. We construct estimators for radial distortions that, using only fast fourier transforms (FFTs) of the overdensity field multipoles for a given survey geometry, compute the power spectrum monopole, quadrupole and hexadecapole, and generalize such estimators to the bispectrum. Using realistic mock catalogs we compare the signal to noise of two estimators for the power spectrum hexadecapole that require different number of FFTs and measure the bispectrum monopole, quadrupole and hexadecapole. The resulting algorithm is very efficient, e.g. the BOSS survey requires about 3 min for ℓ=0,2,4 power spectra for scales up to k=0.3 h Mpc-1 and about 15 additional min for ℓ=0,2,4 bispectra for all scales and triangle shapes up to k=0.2 h Mpc-1 on a single core. The speed of these estimators is essential as it makes possible for one to compute covariance matrices from large number of realizations of mock catalogs with realistic survey characteristics, and paves the way for improved constraints of gravity on cosmological scales, inflation and galaxy bias.

Original language | English (US) |
---|---|

Article number | 083532 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 92 |

Issue number | 8 |

DOIs | |

State | Published - Oct 30 2015 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*92*(8), [083532]. https://doi.org/10.1103/PhysRevD.92.083532

**Fast estimators for redshift-space clustering.** / Scoccimarro, Román.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 92, no. 8, 083532. https://doi.org/10.1103/PhysRevD.92.083532

}

TY - JOUR

T1 - Fast estimators for redshift-space clustering

AU - Scoccimarro, Román

PY - 2015/10/30

Y1 - 2015/10/30

N2 - Redshift-space distortions in galaxy surveys happen along the radial direction, breaking statistical translation invariance. We construct estimators for radial distortions that, using only fast fourier transforms (FFTs) of the overdensity field multipoles for a given survey geometry, compute the power spectrum monopole, quadrupole and hexadecapole, and generalize such estimators to the bispectrum. Using realistic mock catalogs we compare the signal to noise of two estimators for the power spectrum hexadecapole that require different number of FFTs and measure the bispectrum monopole, quadrupole and hexadecapole. The resulting algorithm is very efficient, e.g. the BOSS survey requires about 3 min for ℓ=0,2,4 power spectra for scales up to k=0.3 h Mpc-1 and about 15 additional min for ℓ=0,2,4 bispectra for all scales and triangle shapes up to k=0.2 h Mpc-1 on a single core. The speed of these estimators is essential as it makes possible for one to compute covariance matrices from large number of realizations of mock catalogs with realistic survey characteristics, and paves the way for improved constraints of gravity on cosmological scales, inflation and galaxy bias.

AB - Redshift-space distortions in galaxy surveys happen along the radial direction, breaking statistical translation invariance. We construct estimators for radial distortions that, using only fast fourier transforms (FFTs) of the overdensity field multipoles for a given survey geometry, compute the power spectrum monopole, quadrupole and hexadecapole, and generalize such estimators to the bispectrum. Using realistic mock catalogs we compare the signal to noise of two estimators for the power spectrum hexadecapole that require different number of FFTs and measure the bispectrum monopole, quadrupole and hexadecapole. The resulting algorithm is very efficient, e.g. the BOSS survey requires about 3 min for ℓ=0,2,4 power spectra for scales up to k=0.3 h Mpc-1 and about 15 additional min for ℓ=0,2,4 bispectra for all scales and triangle shapes up to k=0.2 h Mpc-1 on a single core. The speed of these estimators is essential as it makes possible for one to compute covariance matrices from large number of realizations of mock catalogs with realistic survey characteristics, and paves the way for improved constraints of gravity on cosmological scales, inflation and galaxy bias.

UR - http://www.scopus.com/inward/record.url?scp=84946944674&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946944674&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.92.083532

DO - 10.1103/PhysRevD.92.083532

M3 - Article

VL - 92

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 8

M1 - 083532

ER -