Cosmic voids are large underdense regions that, together with galaxy clusters, filaments and walls, build up the large-scale structure of the Universe. The void size function provides a powerful probe to test the cosmological framework. However, to fully exploit this statistics, the void sample has to be properly cleaned from spurious objects. Furthermore, the bias of the mass tracers used to detect these regions has to be taken into account in the size function model. In our work we test a cleaning algorithm and a new void size function model on a set of simulated dark matter halo catalogues, with different mass and redshift selections, to investigate the statistics of voids identified in a biased mass density field. We then investigate how the density field tracers' bias affects the detected size of voids. The main result of this analysis is a new model of the size function, parameterised in terms of the linear effective bias of the tracers used, which is straightforwardly inferred from the large-scale two-point correlation function. This method is a crucial step in exploiting real surveys. The proposed size function model has been accurately calibrated on halo catalogues, and used to validate the possibility to provide forecasts on the cosmological constraints, namely on the matter density contrast, Ω M , and on the normalisation of the linear matter power spectrum, σ 8 , at different redshifts.

Cosmic voids are progressively emerging as a new viable cosmological probe. Their abundance and density profiles are sensitive to modifications of gravity, as well as to dark energy and neutrinos. The main goal of this work is to investigate the possibility of exploiting cosmic void statistics to disentangle the degeneracies resulting from a proper combination of f(R) modified gravity and neutrino mass. We use N-body simulations to analyse the density profiles and size function of voids traced by both dark matter particles and haloes. We find clear evidence of the enhancement of gravity in f(R) cosmologies in the void density profiles at z = 1. However, these effects can be almost completely overridden by the presence of massive neutrinos because of their thermal free streaming. Despite the limited volume of the analysed simulations does not allow us to achieve a statistically relevant abundance of voids larger than 40 Mpc h−1, we find that the void size function at high redshifts and for large voids is potentially an effective probe to disentangle these degenerate cosmological models, which is key in the prospective of the upcoming wide-field redshift surveys.

Cosmic voids are the major volume component in the matter distribution of the Universe. They posses great potential for constraining dark energy as well as for testing theories of gravity. Nevertheless, in spite of their growing popularity as cosmological probes, a gap of knowledge between cosmic void observations and theory still persists. In particular, the void size function models proposed in literature have been proven unsuccessful in reproducing the results obtained from cosmological simulations in which cosmic voids are detected from biased tracers of the density field, undermining the possibility of using them as cosmological probes. The goal of this work is to cover this gap. In particular, we make use of the findings of a previous work in which we have improved the void selection procedure, presenting an algorithm that redefines the void ridges and, consequently, their radius. By applying this algorithm, we validate the volume conserving model of the void size function on a set of unbiased simulated density field tracers. We highlight the difference in the internal structure between voids selected in this way and those identified by the popular VIDE void finder. We also extend the validation of the model to the case of biased tracers. We find that a relation exists between the tracer used to sample the underlying dark matter density field and its unbiased counterpart. Moreover, we demonstrate that, as long as this relation is accounted for, the size function is a viable approach for studying cosmology with cosmic voids.

Aims. We present a cosmological analysis of abundances and stacked weak lensing profiles of galaxy clusters, exploiting the AMICO KiDS-DR3 catalogue. The sample consists of 3652 galaxy clusters with intrinsic richness λ* ≥ 20, over an effective area of 377 deg2, in the redshift range z ∈ [0.1,  0.6]. Methods. We quantified the purity and completeness of the sample through simulations. The statistical analysis has been performed by simultaneously modelling the co-moving number density of galaxy clusters and the scaling relation between the intrinsic richnesses and the cluster masses, assessed through stacked weak lensing profile modelling. The fluctuations of the matter background density, caused by super-survey modes, have been taken into account in the likelihood. Assuming a flat Λ cold dark matter (ΛCDM) model, we constrained Ωm, σ8, S8 ≡ σ8(Ωm/0.3)0.5, and the parameters of the mass-richness scaling relation. Results. We obtained Ωm = 0.24−0.04+0.03, σ8 = 0.86−0.07+0.07, and S8 = 0.78−0.04+0.04. The constraint on S8 is consistent within 1σ with the results from WMAP and Planck. Furthermore, we got constraints on the cluster mass scaling relation in agreement with those obtained from a previous weak lensing only analysis.

The Euclid mission -with its spectroscopic galaxy survey covering a sky area over 15 000 deg 2 in the redshift range 0.9 < z < 1.8 -will provide a sample of tens of thousands of cosmic voids. This paper thoroughly explores for the first time the constraining power of the void size function on the properties of dark energy (DE) from a survey mock catalogue, the official Euclid Flagship simulation. We identified voids in the Flagship light-cone, which closely matches the features of the upcoming Euclid spectroscopic data set. We modelled the void size function considering a state-of-the art methodology: we relied on the volume-conserving (Vdn) model, a modification of the popular Sheth & van de Weygaert model for void number counts, extended by means of a linear function of the large-scale galaxy bias. We found an excellent agreement between model predictions and measured mock void number counts. We computed updated forecasts for the Euclid mission on DE from the void size function and provided reliable void number estimates to serve as a basis for further forecasts of cosmological applications using voids. We analysed two different cosmological models for DE: the first described by a constant DE equation of state parameter, w, and the second by a dynamic equation of state with coefficients w 0 and w a . We forecast 1σ errors on w lower than 10% and we estimated an expected figure of merit (FoM) for the dynamical DE scenario FoM w 0 ,wa = 17 when considering only the neutrino mass as additional free parameter of the model. The analysis is based on conservative assumptions to ensure full robustness, and is a pathfinder for future enhancements of the technique. Our results showcase the impressive constraining power of the void size function from the Euclid spectroscopic sample, both as a stand-alone probe, and to be combined with other Euclid cosmological probes.