Redshift-space effects in voids and their impact on cosmological tests. Part I: the void size function

Cosmic voids are promising cosmological probes. Nevertheless, every cosmological test based on voids must necessary employ methods to identify them in redshift-space. Therefore, systematic effects, such as redshift-space distortions (RSD) and the Alcock-Paczy\'nski effect (AP), are expected to have an impact on the void identification process itself, generating additional distortion patterns in observations. We developed a statistical and theoretical framework that describes physically the void finding mechanism. We used a spherical void finder and made a statistical comparison between real and redshift-space voids. We found that redshift-space voids above the shot noise level have a unique real-space counterpart spanning the same region of space, are systematically bigger and their centres preferentially shifted along the line-of-sight. The expansion effect is a by-product of the 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, which resembles a void dynamics. 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 for the abundance of voids in order to obtain unbiased cosmological constraints from redshift surveys.