### Abstract

We derive the exact relationship, including all nonlinearities, between real-space and redshift-space two-point statistics through the pairwise velocity distribution function. We show using numerical simulations that the pairwise velocity probability distribution function is strongly non-Gaussian at all scales and explain why this is so. We caution that a commonly used ansatz to model the redshift-space power spectrum gives rise to an unphysical distribution of pairwise velocities, and show that it is in general impossible to derive the distribution from measurements of redshift-space clustering. Methods that claim to do this obtain instead something else, whose properties we derive. We provide a general derivation of the large-scale limit of the redshift-space power spectrum and show that it differs from the Kaiser formula by terms that depend on Gaussian and non-Gaussian contributions to the velocity dispersion of large-scale flows. We also show that the large-scale evolution of velocity fields is not well described by linear theory and discuss how this impacts the redshift-space power spectrum. Finally, we stress that using the monopole of the redshift-space power as an indicator of the real-space power spectrum shape can lead to systematic effects in the determination of cosmological parameters; nevertheless a simple procedure is able to recover the large-scale real-space power spectrum rather well.

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

Article number | 083007 |

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

Volume | 70 |

Issue number | 8 |

DOIs | |

State | Published - 2004 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

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

*70*(8), [083007]. https://doi.org/10.1103/PhysRevD.70.083007

**Redshift-space distortions, pairwise velocities, and nonlinearities.** / Scoccimarro, Román.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 70, no. 8, 083007. https://doi.org/10.1103/PhysRevD.70.083007

}

TY - JOUR

T1 - Redshift-space distortions, pairwise velocities, and nonlinearities

AU - Scoccimarro, Román

PY - 2004

Y1 - 2004

N2 - We derive the exact relationship, including all nonlinearities, between real-space and redshift-space two-point statistics through the pairwise velocity distribution function. We show using numerical simulations that the pairwise velocity probability distribution function is strongly non-Gaussian at all scales and explain why this is so. We caution that a commonly used ansatz to model the redshift-space power spectrum gives rise to an unphysical distribution of pairwise velocities, and show that it is in general impossible to derive the distribution from measurements of redshift-space clustering. Methods that claim to do this obtain instead something else, whose properties we derive. We provide a general derivation of the large-scale limit of the redshift-space power spectrum and show that it differs from the Kaiser formula by terms that depend on Gaussian and non-Gaussian contributions to the velocity dispersion of large-scale flows. We also show that the large-scale evolution of velocity fields is not well described by linear theory and discuss how this impacts the redshift-space power spectrum. Finally, we stress that using the monopole of the redshift-space power as an indicator of the real-space power spectrum shape can lead to systematic effects in the determination of cosmological parameters; nevertheless a simple procedure is able to recover the large-scale real-space power spectrum rather well.

AB - We derive the exact relationship, including all nonlinearities, between real-space and redshift-space two-point statistics through the pairwise velocity distribution function. We show using numerical simulations that the pairwise velocity probability distribution function is strongly non-Gaussian at all scales and explain why this is so. We caution that a commonly used ansatz to model the redshift-space power spectrum gives rise to an unphysical distribution of pairwise velocities, and show that it is in general impossible to derive the distribution from measurements of redshift-space clustering. Methods that claim to do this obtain instead something else, whose properties we derive. We provide a general derivation of the large-scale limit of the redshift-space power spectrum and show that it differs from the Kaiser formula by terms that depend on Gaussian and non-Gaussian contributions to the velocity dispersion of large-scale flows. We also show that the large-scale evolution of velocity fields is not well described by linear theory and discuss how this impacts the redshift-space power spectrum. Finally, we stress that using the monopole of the redshift-space power as an indicator of the real-space power spectrum shape can lead to systematic effects in the determination of cosmological parameters; nevertheless a simple procedure is able to recover the large-scale real-space power spectrum rather well.

UR - http://www.scopus.com/inward/record.url?scp=84927755929&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927755929&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.70.083007

DO - 10.1103/PhysRevD.70.083007

M3 - Article

VL - 70

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 8

M1 - 083007

ER -