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 analysing the clustering of more than thirty million galaxies. However, obtaining such constraints requires special care in validating the methodology and efforts to reduce the computational time required through data compression and emulation techniques. In this work, we perform a rigorous validation of the PyBird power spectrum modelling code with both a traditional emulated Full-Modelling approach and the model-independent ShapeFit compression approach. By using cubic box simulations that 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 $\sim0.5\sigma$ level for the $\Lambda$CDM model. Both ShapeFit and Full-Modelling are also consistent with the true $\Lambda$CDM simulation cosmology down to a scale of $k_{\mathrm{max}} = 0.20 h\mathrm{Mpc}^{-1}$ even after including the hexadecapole. For extended models such as the wCDM and the oCDM models, we find that including the hexadecapole can significantly improve the constraints and reduce the modelling errors with the same $k_{\mathrm{max}}$. While their discrepancies between the constraints from ShapeFit and Full-Modelling are more significant than $\Lambda$CDM, they remain consistent within $0.7\sigma$. Lastly, we also show that the constraints on cosmological parameters with the correlation function evaluated from PyBird down to $s_{\mathrm{min}} = 30 h^{-1} \mathrm{Mpc}$ are unbiased and consistent with the constraints from the power spectrum.