Model-independent Calibration for Sound Horizon: Combining Observations of Supernovae and Baryon Acoustic Oscillation Measurements

The sound horizon scale is a key theoretical prediction of the cosmological model that depends on the speed of sound in the baryon-photon fluid and the rate of expansion of the early Universe, before matter and radiation decoupled. Baryon acoustic oscillations (BAOs) offer the direct measurement of this important scale imprinted in the distribution of galaxies. We propose a new model-independent method to calibrate the sound horizon (relative standard ruler) by using the latest observations of Type Ia supernovae (SNe Ia) and 2D BAO measurements. The final result is Mpc h−1 in the framework of the Pantheon SN Ia data set. This result changes to Mpc h−1 when the Pantheon+ data set is used. To highlight our analysis and results, we also use BAO DESI measurements and obtain the best-fitting value Mpc h−1. Note that even without an estimate of the dimensionless Hubble constant h, the combination of 2D BAO and SN Ia data sets already constrains the low-redshift standard ruler scale at the ∼1.26% level (at the ∼1.00% level in the framework of BAO DESI data set). More importantly, it is interesting to note that most of the obtained at high redshifts have systematically larger values: 9 out of 15 results are larger than the result obtained by combining all 2D BAOs. This finding may give us a better understanding of the discordance between the data sets, shed light on the Hubble tension, or reveal the need for new physics beyond the standard cosmological model.