  Survey observations of the three-dimensional locations of galaxies are a
powerful 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 is roughly 10 Gpc3) to be covered, and thus tends to be
expensive. A "sparse sampling" method offers a more affordable solution to this
problem: within a survey footprint covering a given survey volume, Vsurvey, we
observe only a fraction of the volume. The distribution of observed regions
should be chosen such that their separation is smaller than the length scale
corresponding to the wavenumber of interest. Then one can recover the power
spectrum of galaxies with precision expected for a survey covering a volume of
Vsurvey (rather than the volume of the sum of observed regions) with the number
density of galaxies given by 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 with
no window function effect, and deviations from regularly-spaced sampling, which
are unavoidable in realistic surveys, introduce calculable window function
effects and increase the uncertainties of the recovered power spectrum. While
we discuss the sparse sampling method within the context of the forthcoming
Hobby-Eberly Telescope Dark Energy Experiment, the method is general and can be
applied to other galaxy surveys.
