Model independent calibration for sound horizon combining observations of supernovae and transversal BAO measurements

The sound horizon is a key theoretical prediction of the cosmological model that depends on the speed of sound and the rate of expansion in the early universe, before matter and radiation decoupled. The standard ruler for low redshift calibration of baryon acoustic oscillations (BAOs) is a direct measurement that would exist even if the standard cosmological model and the standard assumptions of early physics did not. We propose a new model-independent method to calibrate sound horizon rʰₛ (relative standard ruler) by using the latest observations of SNe Ia and transversal BAO measurements. The final result reports rₛ^h=107. 10^+1. 36-₁. ₃₂ Mpc/h in the framework of the Pantheon dataset. This result changes to rₛ^h=105. 63^+1. 33-₁. ₃₁ Mpc/h when uses Pantheon+ dataset. Note that even without an estimate of dimensionless Hubble constant h, the combination of BAO and SNe Ia datasets already constrain the low-redshift standard ruler scale rₛ^h at the 1. 26\% level. More importantly, it is interesting to find that most of the rₛ^h obtained at high redshifts have a larger value (9 out of 15 results are larger than the result obtained by combining all BAOs). This finding may give us a better understanding of the discordance between the data sets or Hubble tension or reveal new physics beyond the standard model.