The statistics of voids as a tool to constrain cosmological parameters:
  sigma_8 and Omega_m h
  We present a general analytical formalism to calculate accurately several
statistics related to underdense regions in the Universe. The statistics are
computed for dark matter halo and galaxy distributions both in real space and
redshift space at any redshift. Using this formalism, we found that void
statistics for galaxy distributions can be obtained, to a very good
approximation, assuming galaxies to have the same clustering properties as
halos above a certain mass. We deducted a relationship between this mass and
that of halos with the same accumulated number density as the galaxies. We also
found that the dependence of void statistics on redshift is small. For
instance, the number of voids larger than 13 Mpc/h (defined to not contain
galaxies brighter than M_r=-20.4 +5logh change less than 20% between z=1 and
z=0. However, the dependence of void statistics on sigma_8 and Omega_m h is
considerably larger, making them appropriate to develop tests to measure these
parameters. We have shown how to efficiently construct several of these tests
and discussed in detail the treatment of several observational effects. The
formalism presented here along with the observed statistics extracted from
current and future large galaxy redshift surveys will provide an independent
measurement of the relevant cosmological parameters. Combining these
measurements with those found using other methods will contribute to reduce
their uncertainties.
