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Since the early 2000s, the study of the Large Scale Structure of the Universe has become central to cosmology. The European Space Agency Euclid mission promises to significantly advance this field by delivering the most extensive and precise galaxy map to date in optical and infrared bands. However, achieving extreme precision in cosmological measurements, demands rigorous control of systematic effects. Errors in redshift determinations due to noise or spectral line mismatches (noise and line interlopers) can degrade the 2PCF and 3PCF signals. In this study, we assess for the first time the impact of interlopers in the measurement of cosmological parameters with the 3PCF. To do that, we derive and test a new expression for the 3PCF estimator that effectively disentangles the cosmological signal from systematic errors. We implement and test new classes and functions in the CosmoBolognaLib C++ libraries to measure the cross-correlation signal from interlopers for both the 2PCF and 3PCF. Additionally, we assess the impact of redshift interlopers on the 2PCF and 3PCF signals using a galaxy sample from the Euclid official simulations (Flagship 2). Moreover, we model the 2PCF and 3PCF signals considering another large set of Euclid-like simulations (EuclidLargeMocks), comparing pure samples to those contaminated by interlopers. We find that interlopers significantly bias the 2PCF and 3PCF signals, lowering them by more than 30%. Furthermore, we find that cross-correlation signals are crucial in recovering the full 2PCF signal, particularly at low redshifts. We also observe that the linear growth factor, for catalogues affected by interloper contamination is reduced by more than 25% and the linear bias parameter is damped by 20-30%. This work represents the first step in a full self-consistent treatment of realistic data considering systematic effects as expected from the Euclid mission, demonstrating that addressing interloper contamination biases is essential.

The next generation of galaxy redshift surveys will provide us data with unprecedented levels of precision, allowing us to extract new cosmological information from both second- and third-order clustering statistics. For this reason, new theoretical models capable of effectively describing these data sets, as well as new statistical strategies able to reach an advanced accuracy, are required. This Thesis project lies within this context, intending to develop the necessary framework to investigate the combination of two-point correlation function (2PCF) and three-point correlation function (3PCF) of astrophysical objects. We proposed an extension of the redshift-space bispectrum model of Scoccimarro (1999) and a revision of the redshift-space 3PCF model of Slepian and Eisenstein (2017). After having theoretically derived the new 3PCF model and having implemented it in the free software C++/Python libraries for cosmological calculations CosmoBolognaLib (CBL), we performed a validation through a comparison with the 3PCF model used by Veropalumbo et al. (2022). After that, we explored the necessary components to develop a statistical and numerical framework for the probe combination of the 2PCF and 3PCF, a technique which allows us to reduce the statistical errors in the estimates of the cosmological parameters, while breaking some parameter degeneracies. In particular, we applied our pipeline to the 298 MINERVA mock catalogues. We carried out a Bayesian analysis separately on the 2PCF and on the 3PCF. The analysis in real space demonstrates the goodness of our developed models, and shows the potential of the combination of 2PCF and 3PCF in lifting degeneracies in cosmological parameters determination and in increasing the accuracy of the constraints. The analysis in redshift space paves the way to an actual application of this kind of analysis to real data, with several interesting expansions and possible extensions in view of the next large spectroscopic surveys.

The discovery of gravitational waves (GWs) from compact binary coalescences in 2015 unlocked new possibilities for studying the Universe. As their intrinsic loudness can be predicted by General Relativity, GWs provide a direct measurement of the luminosity distance, making them standard sirens. To complement this information and use them as cosmological probes, it is necessary to break the degeneracy between the redshift and the binary masses. In the absence of an electromagnetic counterpart, galaxy catalogues can be used to break this degeneracy, and in this case GWs are referred to as dark sirens. In this Thesis, I used GW events as dark sirens to constrain parameters of different binary black hole mass function (MF) models. I investigated two mock GW catalogues simulating the current O4 and future O5 observing runs by the LIGO-Virgo-KAGRA network, and explored the capability of discriminating between the different MF models with future data. I implemented a new MF model and a nested sampling-based posterior sampling method in the CHIMERA code to estimate Bayesian evidence of different MFs. In addition, I developed code to compute statistical diagnostics such as logB, DIC, and PPC for model selection. Analysing the GW catalogues with available MFs, I constrained their parameters, compared them, and identified the best-fitting model along with the capability to distinguish them. Simultaneously, I conducted a sizing analysis to estimate computational time for GW data analysis. In the last part, I investigated the potential effects of different catalogue assumptions on results, including errors in galaxy catalogue redshift, GW event data smoothing methods, and varying GW event samples. This work paves the way for the optimisation of future GW analysis, proposing strategies to maximise the scientific return and computing capabilities and providing forecasts on expected performances achievable with future GW data.