Abstract: Despite the recent successes of Cosmology in having entered the "Precision Era" there are still open questions. The principal ingredients of the so-called standard ΛCDM model, dark energy (parameterised via Einstein’s cosmological constant, Λ) and cold dark matter (CDM) contribute to ~95\% of the total energy density of the universe. But their underlying nature is still completely unknown. Furthermore, different cosmological observations favor different parameter values, where the most famous discrepancy is the up to 5σ  “Hubble tension" between model-dependent early-time and direct late-time measurements of the Hubble expansion rate H0.

The Dark Energy Spectroscopic Instrument (DESI) survey was launched to unravel the mystery of dark energy by measuring 40 million of distant galaxy and quasar spectra to create the largest, three-dimensional map of the large scale structure of the universe ever obtained. From that map, the DESI collaboration aims to extract both the expansion history and the growth rate of structures history throughout cosmic time. The expansion history is obtained via the so-called "standard ruler" technique: distances (in function of redshift) are measured in units of a characteristic scale, the standard ruler, which is an imprint of the gravity-pressure waves in the early universe leading to the so-called "baryon acoustic oscillations" (BAO). The growth rate of structures is traced by the measurement of the anisotropy of galaxy clustering along and across the line-of-sight, which is induced by the peculiar velocities of galaxies impacting the redshift measurements from their spectra. As a consequence, distances inferred from these redshifts are distorted, hence this effect is called "redshift-space distortions" (RSD).

In the first part of this thesis we present a method to blind the galaxy catalogs to mimic different BAO and RSD signals. Upcoming DESI data will benefit from blinding in order to remove the impact of confirmation bias on cosmological results. In the second part, we elevate the established way how BAO and RSD analyses are performed towards including another observable, the shape “m" of the clustering signal as function of galaxy separations. Both parts of this thesis stress the importance of model-agnosticism in the context of large surveys and cosmological tensions. They play a crucial role for the DESI survey cosmological analysis providing a road to transition from the "Precision Era" to the "Accuracy Era" of cosmology.