eng The ωCDM model has long been established as the standard model of cosmology, describing our observations of both early and late timeUniverse in a remarkably accurate and simple way. However, the nature of most of its components–dark matter and dark energy–is fundamentally unknown. Meanwhile, tensions such as those observed in the Hubble constant measurements 1, 2 or in the dark energy behaviour 3, 4 become increasingly significant. Most of the cosmological results that have been responsible for the development and testing of the ωCDM model have traditionally involved some form of two-point statistics–either the two-point correlation function or its Fourier counterpart, the power spectrum. Two-point statistics cannot, by definition, exploit all the information encoded in the cosmic density field, since the effect of gravity transfers some of this information to higher-order statistics. The lower next-order statistics are the three-point correlation function and its equivalent in Fourier space, the bispectrum. As our observational capabilities advance with the latest generation of surveys, such as the Dark Energy Spectroscopic Instrument (DESI) 5, now is a key moment to push beyond traditional two-point statistics. This thesis works towards this mission, by developing a framework for performing joint analyses involving both the power spectrum and bispectrum of large-scale structure. In the first part of this thesis, we provide the building blocks of our framework: we design the GEO-FPT model in 6, which is based on perturbation theory while incorporating corrections inspired by geometrical properties of the bispectrum that we see in cosmological simulations. This allows us to extend our bispectrum modelling into the mildly non-linear regime, which translates into a significant increase of its constraining power on cosmological parameters, such as the size and shape of the baryon acoustic oscillations (BAO), the growth rate of structure, and the imprint of early- and late-time physics on the shape of the power spectrum. Additionally, in 7 we explore another important aspect for our proposed joint power spectrum and bispectrum analysis, the covariance matrix. In particular, we test the validity of a common approximation: only considering the elements in the covariance diagonal. Such an approach results, within our analysis choices, in an underestimation of up to → 10% in the recovered cosmological parameters error bars. In the second part of this thesis, we make the non-trivial transition towards implementing our pipeline to real galaxy data, targeting the DESI Data Release 1 (DR1).We start by addressing a distinctive feature of the DESI analysis, which is the fact that, with the goal of mitigating confirmation bias, all official analyses are performed with data that is blinded at a catalogue level, until all choices are fixed. In 8,we test the effect in the bispectrum of the two most relevant parts (for our analysis) of the DESI official blinding scheme.We find that our power spectrum and bispectrum data-vector recovers the predicted constraints on the blinded data, consequently enabling us to follow the DESI blinding policy in our bispectrum analysis. Finally, in which is the culmination of this thesis, in 9 we perform full-shape analysis of the power spectrum and bispectrum of DESI DR1. By using the data from Luminous Red Galaxies and quasars, we effectively trace →10 billion years of Universe evolution. After rigorously quantifying the systematic error budget, we constrain cosmological parameters to a higher degree of precision than the existing analyses that were based solely on two-point statistics. These measurements are compatible with the official DESI DR1 power spectrum results 10 and with the fiducial Planck ωCDM cosmology 2.We will continue to explore the compatibility of our results with ωCDM and its extensions in a follow-up work 11. This thesis addresses the challenges and necessity of including higherorder statistics into the analyses of current and future galaxy surveys, in a step towards using the data to its full potential. This can only elevate our ability to test the strengths and weaknesses of the ωCDM model and its myriad alternatives, with the ultimate goal of deepening our understanding of the fundamental physics driving the Universe that we see today.
Sergi Novell Masot (Mon,) studied this question.