Effects of long-wavelength fluctuations in large galaxy surveys
  In order to capture as much information as possible large galaxy surveys have
been increasing their volume and redshift depth. To face this challenge theory
has responded by making cosmological simulations of huge computational volumes
with equally increasing the number of dark matter particles and supercomputing
resources. Thus, it is taken for granted that the ideal situation is when a
single computational box encompasses the whole effective volume of the
observational survey, e.g., ~50 Gpch^3 for the DESI and Euclid surveys. Here we
study the effects of missing long-waves in a finite volume using several
relevant statistics: the abundance of dark matter halos, the PDF, the
correlation function and power spectrum, and covariance matrices. Finite volume
effects can substantially modify the results if the computational volumes are
less than ~(500Mpch)^3. However, the effects become extremely small and
practically can be ignored when the box-size exceeds ~1Gpch^3. We find that the
average power spectra of dark matter fluctuations show remarkable lack of
dependence on the computational box-size with less than 0.1% differences
between 1Gpch and 4Gpch boxes. No measurable differences are expected for the
halo mass functions for these volumes. The covariance matrices are scaled
trivially with volume, and small corrections due to super-sample modes can be
added. We conclude that there is no need to make those extremely large
simulations when a box-size of 1-1.5Gpch is sufficient to fulfil most of the
survey science requirements.
