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ABSTRACT This paper provides a comprehensive overview of how fitting of baryon acoustic oscillations (BAO) is carried out within the upcoming Dark Energy Spectroscopic Instrument’s (DESI) 2024 results using its DR1 data set, and the associated systematic error budget from theory and modelling of the BAO. We derive new results showing how non-linearities in the clustering of galaxies can cause potential biases in measurements of the isotropic ($$\alpha _{\mathrm{iso}}$$) and anisotropic ($$\alpha _{\mathrm{ap}}$$) BAO distance scales, and how these can be effectively removed with an appropriate choice of reconstruction algorithm. We then demonstrate how theory leads to a clear choice for how to model the BAO and develop, implement, and validate a new model for the remaining smooth-broad-band (i.e. without BAO) component of the galaxy clustering. Finally, we explore the impact of all remaining modelling choices on the BAO constraints from DESI using a suite of high-precision simulations, arriving at a set of best practices for DESI BAO fits, and an associated theory and modelling systematic error. Overall, our results demonstrate the remarkable robustness of the BAO to all our modelling choices and motivate a combined theory and modelling systematic error contribution to the post-reconstruction DESI BAO measurements of no more than 0.1 per cent (0.2 per cent) for its isotropic (anisotropic) distance measurements. We expect the theory and best practices laid out to here to be applicable to other BAO experiments in the era of DESI and beyond. 

Abstract We present cosmological constraints from the sample of Type Ia supernovae (SNe Ia) discovered and measured during the full 5 yr of the Dark Energy Survey (DES) SN program. In contrast to most previous cosmological samples, in which SNe are classified based on their spectra, we classify the DES SNe using a machine learning algorithm applied to their light curves in four photometric bands. Spectroscopic redshifts are acquired from a dedicated follow-up survey of the host galaxies. After accounting for the likelihood of each SN being an SN Ia, we find 1635 DES SNe in the redshift range 0.10 <z< 1.13 that pass quality selection criteria sufficient to constrain cosmological parameters. This quintuples the number of high-qualityz> 0.5 SNe compared to the previous leading compilation of Pantheon+ and results in the tightest cosmological constraints achieved by any SN data set to date. To derive cosmological constraints, we combine the DES SN data with a high-quality external low-redshift sample consisting of 194 SNe Ia spanning 0.025 <z< 0.10. Using SN data alone and including systematic uncertainties, we find Ω_M= 0.352 ± 0.017 in flat ΛCDM. SN data alone now require acceleration (q₀< 0 in ΛCDM) with over 5σconfidence. We find $({\mathrm{\Omega }}_{\mathrm{M}},w)=({0.264}_{-0.096}^{+0.074},-{0.80}_{-0.16}^{+0.14})$in flatwCDM. For flatw₀w_aCDM, we find $({\mathrm{\Omega }}_{\mathrm{M}},w_0,w_a)=({0.495}_{-0.043}^{+0.033},-{0.36}_{-0.30}^{+0.36},-{8.8}_{-4.5}^{+3.7})$, consistent with a constant equation of state to within ∼2σ. Including Planck cosmic microwave background, Sloan Digital Sky Survey baryon acoustic oscillation, and DES 3 × 2pt data gives (Ω_M,w) = (0.321 ± 0.007, −0.941 ± 0.026). In all cases, dark energy is consistent with a cosmological constant to within ∼2σ. Systematic errors on cosmological parameters are subdominant compared to statistical errors; these results thus pave the way for future photometrically classified SN analyses.