How to evade the sample variance limit on measurements of redshift-space distortions

By P. Mcdonald, Uros Seljak. 2008

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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., ≃ 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.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/564a73c508acb24028e605c169c53c563f40cb0b

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Citations in the corpus

DESI and other Dark Energy experiments in the era of neutrino mass measurements (2013, methodology): “We simply give the estimated constraining power for the main redshift surveys, based on the power spectrum, for the local model of non-Gaussianity, following [65, 145].”
The DESI Bright Galaxy Survey: Final Target Selection, Design, and Validation (2022, background): “From the three-dimensional spatial clustering of these galaxies and quasars, DESI will precisely measure the expansion history of the universe using baryon acoustic oscillations (BAO) and the growth of structure using redshift-space distortions (RSDs).”
Observational probes of cosmic acceleration (2012, methodology): “The cross-correlation approach is more powerful if the spectroscopic survey includes galaxies with a wide range of bias factors (McDonald and Seljak, 2009), e.g., a mix of massive absorption-line galaxies and lower mass emission-line galaxies.”
Galaxy And Mass Assembly (GAMA): improved cosmic growth measurements using multiple tracers of large-scale structure (2013, background): “…of multiple galaxy tracers across a volume of space allows improved statistical errors in the measurements of certain cosmological parameters (McDonald & Seljak 2009; Seljak 2009; White, Song & Percival 2009; Gil-Marin et al. 2010; Bernstein & Cai 2011; Hamaus, Seljak & Desjacques 2012;…”
Primordial non-Gaussianity from the large-scale structure (2010, background): “By comparing differently biased tracers of the same surveyed volume [162, 163] and suitably weighting galaxies (by the mass of their host halo for instance) [164, 165], it should be possible to circumvent these problems and considerably improve the detection level.”
Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory (2020, background): “The overlap in redshifts between samples enables techniques to combine multiple tracers and reduce the effects of sample variance (McDonald & Seljak 2009; Seljak 2009).”
The DESI Experiment Part I: Science,Targeting, and Survey Design (2016, methodology): “In this case it may possible to cancel sampling variance, which is the dominant source of error on large scales [160, 161], but due to low number density this will have to include an additional tracer of structure, potentially combining with the LSST and DES data.”
THE SDSS-IV EXTENDED BARYON OSCILLATION SPECTROSCOPIC SURVEY: OVERVIEW AND EARLY DATA (2015, methodology): “Because of the overlap in redshift range between the ELG sample and the LRG and quasar samples, the eBOSS data also enable techniques such as those introduced in McDonald & Seljak (2009) and Seljak (2009) to combine multiple tracers and reduce the effects of sample variance.”
Testing gravity using cosmic voids (2014, background): “…has been promoted by the combination of redshift space distortion with lensing,which is another powerful way of constraining the linear growth and hence gravity (McDonald & Seljak 2009; Bernstein & Cai 2011; Cai & Bernstein 2012; Gaztañaga et al. 2012; de Putter et al. 2013; Kirk et al. 2013).”