Modeling the void size function and its cosmology dependence in galaxy surveys

In the field of large scale structure, cosmic voids are gaining more and more importance as useful probes of cosmology and fundamental physics. This is partly due to the more linear gravitational evolution as compared to their overdense halo counterparts. However, the models and parameters used to describe cosmic voids are still not univocal, and their analysis is often limited to the largest sizes. This ignores the so- called void-in-cloud effect, describing smaller voids embedded in overdense surroundings. The aim of this thesis is to model the void size function including the void-in-cloud effect, and to study its cosmology dependence. In order to do so, we generate different void catalogs from the PATCHY mocks of SDSS BOSS DR12 using the void finder VIDE, each assuming a different value of the matter density parameter m for the transformation from redshifts to distances. We adopt a multivariate analysis to remove spurious voids by comparing their properties with voids from a random catalog. We fit different models for the void size function proposed in literature to the void abundance of the cleaned catalog. Each fit is performed using a MCMC with three free parameters: the linear threshold for void formation δv, the linear threshold for collapse δc, and the rescaling factor rs. We find that the various models exhibit different levels of agreement with the data, and a different behaviour of the parameters as a function of Ωm. The Vdn model shows an anomaly in its parameters corresponding to the true value of Ωm used in the construction of the mock galaxy catalog, indicating a way to recognise it among the different cosmologies. After the application an Alcock- Paczynski correction to the catalogs, the Vdn model shows a residual dependence of the fitting parameters upon the value of Ωm. The results of this work underline the importance of studying the void-in-cloud effect in order to understand the distribution of cosmic voids in galaxy surveys.