Fiducial-Cosmology-dependent systematics for the DESI 2024 Full-Shape Analysis

We assess the impact of the fiducial cosmology choice on cosmological inference from full-shape (FS) fits of the galaxy power spectrum in the DESI 2024 Data Release 1 (DR1). Using a suite of AbacusSummit DR1 mock catalogues based on the Planck 2018 best-fit cosmology, we quantify potential systematic shifts introduced by analysing the data under five secondary cosmologies - featuring variations in matter density, thawing dark energy, higher effective number of neutrino species, reduced clustering amplitude, and the DESI DR1 BAO best-fit $w_0w_a$CDM cosmology - relative to DESI's baseline Planck 2018 cosmology. We investigate two complementary FS analysis approaches: full-modelling (FM) and ShapeFit (SF), each with distinct sensitivities to the assumed fiducial model. Across all tracers, we find for FM that systematic shifts induced by fiducial cosmology mismatches remain well below the DESI DR1 statistical uncertainties, with maximum deviations of 0.22$\sigma_\mathrm{DR1}$ in $\Lambda$CDM scenarios and 0.12$\sigma_\mathrm{DR1+SN}$ when including SN Ia mock data in extended $w_0w_a$CDM fits. For SF, the shifts in the compressed parameters remain below $0.45\sigma_\mathrm{DR1}$ for all tracers and cosmologies.