Redshift-space effects in voids and their impact on cosmological tests.
  Part I: the void size function
  Voids are promising cosmological probes. Nevertheless, every cosmological
test based on voids must necessarily employ methods to identify them in
redshift space. Therefore, redshift-space distortions (RSD) and the
Alcock-Paczynski effect (AP) have an impact on the void identification process
itself generating distortion patterns in observations. Using a spherical void
finder, we developed a statistical and theoretical framework to describe
physically the connection between the identification in real and redshift
space. We found that redshift-space voids above the shot noise level have a
unique real-space counterpart spanning the same region of space, they are
systematically bigger and their centres are preferentially shifted along the
line of sight. The expansion effect is a by-product of RSD induced by tracer
dynamics at scales around the void radius, whereas the off-centring effect
constitutes a different class of RSD induced at larger scales by the global
dynamics of the whole region containing the void. The volume of voids is also
altered by the fiducial cosmology assumed to measure distances, this is the AP
change of volume. These three systematics have an impact on cosmological
statistics. In this work, we focus on the void size function. We developed a
theoretical framework to model these effects and tested it with a numerical
simulation, recovering the statistical properties of the abundance of voids in
real space. This description depends strongly on cosmology. Hence, we lay the
foundations for improvements in current models of the abundance of voids in
order to obtain unbiased cosmological constraints from redshift surveys.
