Towards a joint modelling of second- and third-order clustering statistics of the Large Scale Structure

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.