Quantifying cosmic variance
  We determine an expression for the cosmic variance of any "normal" galaxy
survey based on examination of M* +/- 1 mag galaxies in the SDSS DR7 data cube.
We find that cosmic variance will depend on a number of factors principally:
total survey volume, survey aspect ratio, and whether the area surveyed is
contiguous or comprised of independent sight-lines. As a rule of thumb cosmic
variance falls below 10% once a volume of 10^7h_0.7^-3Mpc^3 is surveyed for a
single contiguous region with a 1:1 aspect ratio. Cosmic variance will be lower
for higher aspect ratios and/or non-contiguous surveys. Extrapolating outside
our test region we infer that cosmic variance in the entire SDSS DR7 main
survey region is ~7% to z < 0.1. The equation obtained from the SDSS DR7 region
can be generalised to estimate the cosmic variance for any density measurement
determined from normal galaxies (e.g., luminosity densities, stellar mass
densities and cosmic star-formation rates) within the volume range 10^3 to 10^7
h^-3_0.7Mpc^3. We apply our equation to show that 2 sightlines are required to
ensure cosmic variance is <10% in any ASKAP galaxy survey (divided into dz ~0.1
intervals, i.e., ~1 Gyr intervals for z <0.5). Likewise 10 MeerKAT sightlines
will be required to meet the same conditions. GAMA, VVDS, and zCOSMOS all
suffer less than 10% cosmic variance (~3%-8%) in dz intervals of 0.1, 0.25, and
0.5 respectively. Finally we show that cosmic variance is potentially at the
50-70% level, or greater, in the HST Ultra Deep Field depending on assumptions
as to the evolution of clustering. 100 or 10 independent sightlines will be
required to reduce cosmic variance to a manageable level (<10%) for HST ACS or
HST WFC3 surveys respectively (in dz ~ 1 intervals). Cosmic variance is
therefore a significant factor in the z>6 HST studies currently underway.
