Reducing sample variance: halo biasing, non-linearity and stochasticity

Hector Gil-Marin, Christian Wagner, Licia Verde, Raul Jimenez, Alan F. Heavens

Research output: Contribution to journalArticlepeer-review

Abstract

Comparing clustering of differently biased tracers of the dark matter distribution offers the opportunity to reduce the sample or cosmic variance error in the measurement of certain cosmological parameters. We develop a formalism that includes bias non-linearities and stochasticity. Our formalism is general enough that it can be used to optimize survey design and tracers selection and optimally split (or combine) tracers to minimize the error on the cosmologically interesting quantities. Our approach generalizes the one presented by McDonald & Seljak of circumventing sample variance in the measurement of f equivalent to d ln D/d ln a. We analyse how the bias, the noise, the non-linearity and stochasticity affect the measurements of Df and explore in which signal-to-noise regime it is significantly advantageous to split a galaxy sample in two differently biased tracers. We use N-body simulations to find realistic values for the parameters describing the bias properties of dark matter haloes of different masses and their number density. We find that, even if dark matter haloes could be used as tracers and selected in an idealized way, for realistic haloes, the sample variance limit can be reduced only by up to a factor Sigma(2tr)/Sigma(1tr) similar or equal to 0.6. This would still correspond to the gain from a three times larger survey volume if the two tracers were not to be split. Before any practical application one should bear in mind that these findings apply to dark matter haloes as tracers, while realistic surveys would select galaxies: the galaxy-host halo relation is likely to introduce extra stochasticity, which may reduce the gain further.

Original languageEnglish
Pages (from-to)772-790
Number of pages19
JournalMonthly Notices of the Royal Astronomical Society
Volume407
Issue number2
Early online date17 Jun 2010
DOIs
Publication statusPublished - 11 Sep 2010

Keywords

  • cosmological parameters
  • cosmology: theory
  • large-scale structure of Universe
  • GALAXY REDSHIFT SURVEY
  • LARGE-SCALE BIAS
  • POWER-SPECTRUM
  • MATTER DENSITY
  • DARK-MATTER
  • CONSTRAINTS
  • DISTORTIONS
  • UNIVERSE
  • SPACE
  • PEAKS

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