Testing the FLRW metric with Hubble and transverse BAO measurements

The cosmological principle is one of the fundamental assumptions of the standard model of cosmology (SCM), and it allows us to describe cosmic distances and clocks by using the Friedmann-Lema\^tre-Roberton-Walker (FLRW) metric. Thus, it is essential to test the FLRW metric with cosmological observations to verify the validity of the SCM. In this work, we perform tests of the FLRW metric by comparing the observational comoving angles between the Hubble H (z) and the transversal baryon acoustic oscillation (BAO) measurements. The Gaussian process is employed to reconstruct the Hubble H (z) measurements and the angular diameter distance (ADD) from the transversal BAO data. A nonparametric method is adopted to probe the possible deviations from the FLRW metric at any redshift by comparing the comoving distances from the reconstructed Hubble H (z) measurements with the ADD reconstructed from the transversal BAO data. Then, we propose two types of parametrizations for the deviations from the FLRW metric, and test the FLRW metric by using the priors of specific sound horizon scales. To avoid the bias caused by the prior of a specific sound horizon scale, we perform the consistency test with a flat prior of the sound horizon scale. We find that there is a concordance between the FLRW metric and the observational data by using parametric and nonparametric methods, and the parametrizations can be employed to test the FLRW metric in a new way independent of the sound horizon scale.