Determination of the Hubble Constant and Sound Horizon from Dark Energy Spectroscopic Instrument Year 1 and Dark Energy Survey Year 6 Baryon Acoustic Oscillation

We perform new measurements of the expansion rate and the sound horizon at the end of the baryon decoupling, and derive constraints on cosmic key parameters in the framework of the ΛCDM model, wCDM model, non-flat ΛCDM model and the phenomenological emergent dark energy (PEDE) model. We keep rd and H0 completely free, and use the recent Dark Energy Spectroscopic Instrument (DESI) Year 1 and Dark Energy Survey (DES) Year 6 BAO measurements in the effective redshift range 0.3<z<2.33, combined with the compressed form of the Pantheon sample of Type Ia supernovae, the latest 34 observational H(z) measurements based on the differential age method, and the recent H0 measurement from SH0ES 2022 as an additional Gaussian prior. Combining BAO data with the observational H(z) measurements, and the Pantheon SNe Ia data, we obtain H0=69.70±1.11 km s−1Mpc−1, rd=147.14±2.56 Mpc in flat ΛCDM model, H0=70.01±1.14 km s−1Mpc−1, rd=146.97±2.45 Mpc in PEDE model. The spatial curvature is Ωk=0.023±0.025, and the dark energy equation of state is w=−1.029±0.051, consistent with a cosmological constant. We apply the Akaike information and the Bayesian information criterion test to compare the four models, and see that the PEDE model performs better.