We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter β ≡ b−1f ≡ b−1d ln D/d ln a (where D is the growth factor and a the expansion factor), to, as the signal-to-noise (S/N) of a survey increases, much better precision than one could achieve with a single tracer (to arbitrary precision in the low noise limit). In combination with the power spectrum of the tracers this would allow a more precise measurement of the bias-free velocity divergence power spectrum, f2Pm, with the ultimate, zero noise limit, being that f2Pm can be measured as well as would be possible if velocity divergence was observed directly, with maximum rms improvement factor ~ [5.2(β2+2β+2)/β2]1/2 (e.g., simeq 10 times better than a single tracer with β = 0.4). This would allow a determination of fD as a function of redshift with an error as low as ~ 0.1% (again, in the idealized case of the zero noise limit). The ratio b2/b1 can be determined with an even greater precision than β, potentially producing, when measured as a function of scale, an exquisitely sensitive probe of the onset of non-linear bias. We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity. Currently planned redshift surveys are typically designed with S/N ~ 1 on scales of interest, which severely limits the usefulness of our method. Our results suggest that there are potentially large gains to be achieved from technological or theoretical developments that allow higher S/N, or, in the long term, surveys that simply observe a higher number density of galaxies.

McDonald, P; Seljak, U (2009). *How to evade the sample variance limit on measurements of redshift-space distortions.* Journal of Cosmology and Astroparticle Physics, 10:007 .

## Abstract

We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter β ≡ b−1f ≡ b−1d ln D/d ln a (where D is the growth factor and a the expansion factor), to, as the signal-to-noise (S/N) of a survey increases, much better precision than one could achieve with a single tracer (to arbitrary precision in the low noise limit). In combination with the power spectrum of the tracers this would allow a more precise measurement of the bias-free velocity divergence power spectrum, f2Pm, with the ultimate, zero noise limit, being that f2Pm can be measured as well as would be possible if velocity divergence was observed directly, with maximum rms improvement factor ~ [5.2(β2+2β+2)/β2]1/2 (e.g., simeq 10 times better than a single tracer with β = 0.4). This would allow a determination of fD as a function of redshift with an error as low as ~ 0.1% (again, in the idealized case of the zero noise limit). The ratio b2/b1 can be determined with an even greater precision than β, potentially producing, when measured as a function of scale, an exquisitely sensitive probe of the onset of non-linear bias. We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity. Currently planned redshift surveys are typically designed with S/N ~ 1 on scales of interest, which severely limits the usefulness of our method. Our results suggest that there are potentially large gains to be achieved from technological or theoretical developments that allow higher S/N, or, in the long term, surveys that simply observe a higher number density of galaxies.

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## Additional indexing

Other titles: | How to measure redshift-space distortions without sample variance |
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Item Type: | Journal Article, refereed, original work |

Communities & Collections: | 07 Faculty of Science > Institute for Computational Science |

Dewey Decimal Classification: | 530 Physics |

Uncontrolled Keywords: | power spectrum; dark matter; surveys galaxies; dark energy theory |

Language: | English |

Date: | October 2009 |

Deposited On: | 27 Feb 2010 16:34 |

Last Modified: | 05 Apr 2016 13:56 |

Publisher: | Institute of Physics Publishing |

ISSN: | 1475-7516 |

Publisher DOI: | 10.1088/1475-7516/2009/10/007 |

Related URLs: | http://arxiv.org/abs/0810.0323 |

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