A comparison between Shapefit compression and Full-Modelling method with PyBird for DESI 2024 and beyond

DESI aims to provide one of the tightest constraints on cosmological parameters by analyzing the clustering of more than thirty million galaxies. However, obtaining such constraints requires special care in validating the analysis methods, and efforts to reduce the computational time required through techniques such as data compression and emulation. In this work, we perform a precision validation of the PyBird power spectrum modelling code with both a traditional, but emulated, Full-Modelling approach and the model-independent Shapefit compression approach. Using cubic simulations, which accurately reproduce the clustering and precision of the DESI survey, we find that the cosmological constraints from Shapefit and Full-Modelling are consistent with each other at the ∼0.3σ level. Both Shapefit and Full-Modelling are also consistent with the true ΛCDM simulation cosmology, even when including the hexadecapole, down to a scale k_max = 0.20 h Mpc^-1. For extended models such as the wCDM and the oCDM models, we find including the hexadecapole can significantly improve the constraints and reduce the systematic errors with the same k_max. Furthermore, we also show that the constraints on cosmological parameters with the correlation function evaluated from PyBird down to s_min = 30 h^-1Mpc are unbiased, and consistent with the constraints from the power spectrum.