Cosmic acceleration and the Hubble tension from baryon acoustic oscillation data

We investigate the null tests of cosmic accelerated expansion by using the Baryon Acoustic Oscillation (BAO) data measured by the Dark Energy Spectroscopic Instrument (DESI) and reconstruct the dimensionless Hubble parameter $E(z)$ from the DESI BAO Alcock-Paczynski (AP) data using Gaussian process to perform the null test. We find strong evidence of accelerated expansion from the DESI BAO AP data. By reconstructing the deceleration parameter $q(z)$ from the DESI BAO AP data, we find that accelerated expansion persisted until $z \lesssim 0.7$ with a 99.7\% confidence level. Additionally, to provide insights into the Hubble tension problem, we propose combining the reconstructed $E(z)$ with $D_H/r_d$ data to derive the model-independent result $r_d h=99.8\pm 3.1$ Mpc. This result is consistent with measurements from cosmic microwave background (CMB) anisotropies using the $\Lambda$CDM model. We also propose a model-independent method for reconstructing the comoving angular diameter distance $D_M(z)$ from the distance modulus $\mu$ using SNe Ia data and combining this result with DESI BAO data of $D_M/r_d$ to constrain the value of $r_d$. We find that the value of $r_d$ derived from this model-independent method is smaller than that obtained from CMB measurements, with a significant discrepancy of at least 4.17$\sigma$. All the conclusions drawn in this paper are independent of cosmological models and gravitational theories.