Reconstruction of dark energy using DESI DR2

Using a model-independent Gaussian process (GP) method to reconstruct the dimensionless luminosity distance $D$ and its derivatives, we derive the evolution of the dimensionless Hubble parameter $E$, the deceleration parameter $q$, and the state parameter $w$ of dark energy. We utilize the PantheonPlus, SH0ES, and Gamma Ray Burst (GRB) data to derive the dimensionless luminosity distance $D$. Additionally, we employ observational $H(z)$ data (OHD) and baryon acoustic oscillations (BAO) from Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) to obtain the first derivative of the dimensionless luminosity distance $D^{'}$. To obtain the reconstructed $D$ and $D^{'}$, we utilize the fiducial value from each dataset, with particular emphasis on the varying $H_0$. According to the reconstruction results obtained from PantheonPlus+SH0ES+GRB+OHD and PantheonPlus+SH0ES+GRB+OHD+DESI data, we find that $E$ are consistent with the predictions of the $\Lambda$CDM model at a $2\sigma$ confidence level within the redshift range of $z<2$. However, the reconstruction results for $q$ exhibit deviations from the $\Lambda$CDM model in the range of $z<0.3$. Furthermore, we observe that the mean value of $w$ exhibits evolving behavior, transiting from $w < -1$ to $w > -1$ around $z_{\rm wt}=0.464^{+0.235}_{-0.120}$. Combining data from DESI DR2 can slightly enhance the accuracy of our constraints.