Possible evidences for physics beyond $\mathrm{\Lambda }$CDM from DESI DR2 data

We analyze DESI DR2 data with a model-independent method and find that: (a) the expansion of the universe may speed up with a confidence level more than 2.3 $\sigma$ at redshift $z_{51}\in (0.51,0.955)$; (b) the expansion of the universe may speed down with a confidence level greater than 1.7 $\sigma$ at redshift $z_{75}\in (0.955,1.484)$; © $w_{\mathrm{x}}\le w_{\mathrm{t}}<-1$ with confidence level exceeding 1.6 $\sigma$ at redshift $z_{53}\in (0.922,0.955)$.