Galaxy redshift surveys with sparse sampling

Abstract

Survey observations of the three-dimensional locations of galaxies are apowerful approach to measure the distribution of matter in the universe,which can be used to learn about the nature of dark energy,physics of inflation, neutrino masses, etc. A competitive survey, however,requires a large volume (e.g., Vsurvey ∼ 10Gpc3) tobe covered, and thus tends to be expensive.A ``sparse sampling'' method offers a more affordable solution to thisproblem: within a survey footprint covering a given survey volume,Vsurvey, we observe only a fraction of the volume. The distributionof observed regions should be chosen such that their separation is smaller thanthe length scale corresponding to the wavenumber of interest. Thenone can recover the power spectrum of galaxies with precision expected fora survey covering a volume of Vsurvey (rather than the volumeof the sum of observed regions) with the number density of galaxies givenby the total number of observed galaxies divided by Vsurvey(rather than the number density of galaxies within an observed region).We find that regularly-spaced sampling yields an unbiased power spectrum withno window function effect, and deviations from regularly-spaced sampling,which are unavoidable in realistic surveys, introduce calculable windowfunction effects and increase the uncertainties of the recovered power spectrum.On the other hand, we show that the two-point correlation function (paircounting) is not affected by sparse sampling.While we discuss the sparse sampling method within the context of theforthcoming Hobby-Eberly Telescope Dark Energy Experiment, the method is general and can beapplied to other galaxy surveys.