Reconstructing dark energy with model independent methods after DESI DR2 BAO

In this paper, we employ two model-independent approaches, including redshift binning method and polynomial interpolation method, to reconstruct dark energy (DE) equation of state (EoS) $w(z)$ and DE density function $f(z)$. Our analysis incorporates data from the Dark Energy Spectroscopic Instrument (DESI) data release 2, Cosmic Microwave Background (CMB) distance priors from Planck 2018 and Atacama Cosmology Telescope data release 6, and three Type Ia supernovae (SN) compilations (PantheonPlus, Union3, and DESY5). To ensure model independence, we adopt three redshift binning schemes (n=3, 4, 5) and three polynomial interpolation schemes with the same number of nodes (n=3, 4, 5). Our main conclusions are as follows: 1) After taking into account DESI data, there is a clear trend that DE should evolve with redshift (with deviations from the cosmological constant reaching at least a $2.13σ$ confidence level), indicating that current observations favor a dynamical DE. 2) In the redshift range $0.5 < z < 1.5$, the DE EoS w(z) exhibits a decreasing trend and crosses the phantom divide $w=-1$, suggesting quintom-like behavior. 3) The DE density f(z) first increases at low redshift, reaching a hump around $z\approx 0.5$, and then decreases at $0.5 < z < 1.5$, with a rapid decrease at $z>1.0$. 4) For $z > 1.5$, current data are insufficient to place strong constraints on the evolution of DE, resulting in large uncertainties in the DE reconstruction. It must be emphasized that, these four main conclusions are independent of specific reconstruction models, and are insensitive to the choice of SN compilations.