Title: The Self-Consistency of DESI Analysis and Comment on "Does DESI 2024 Confirm $Λ$CDM?"

Abstract: We demonstrate that the constraints on the evolution of dark energy implemented by the DESI collaboration may be insufficient or incomplete using their own BAO data. Using large enough prior ranges for the present-day equation of state of dark energy $\omega_0$ and amplitude of dark energy evolution $\omega_a$, we obtain the complete $1\,\sigma$ and $2\,\sigma$ constraints $\omega_0=1.04^{+0.91+2.00}_{-1.00-1.90}$ and $\omega_a=-7.4^{+3.8+6.8}_{-3.2-7.3}$ indicating a beyond $2\,\sigma$ preference of quintessence-like dark energy today and an evidence of evolving dark energy at beyond $2\,\sigma$ CL, respectively. Our results are different from $\omega_0=-0.55^{+0.39}_{-0.21}$ and the $2\,\sigma$ upper limit $\omega_a<-1.32$ reported by the DESI collaboration \cite{DESI:2024mwx}. Employing a data combination of cosmic microwave background, DESI BAO and type Ia supernova, we obtain the $1\,\sigma$, $2\,\sigma$ and $3\,\sigma$ constraints $\omega_0=-0.707^{+0.089+0.18+0.24}_{-0.089-0.17-0.22}$ and $\omega_a=-1.09^{+0.38+0.67+0.82}_{-0.31-0.72-1.00}$, which reveals a $\sim4\,\sigma$ evidence of dynamical dark energy when the redshift $z\lesssim0.1$. We verify that the BAO data point from luminous red galaxies at the effective redshift $z_{\rm eff}=0.51$ hardly affects the joint constraint from the data combination of cosmic microwave background, DESI BAO and type Ia supernova. We also point out the shortcomings and advantages of the binning method widely used in cosmological analyses.