Impact of a negative cosmological constant on the reconstruction of dark energy in light of DESI BAO data

An anti-de Sitter vacuum, corresponding to a negative cosmological constant (NCC), might coexist with one evolving positive dark energy component at low redshift and is hinted by the latest DESI observations. In this paper, we use two methods, $\mathit{\text{redshift-binned}}$ and $\mathit{\text{Gaussian}}\mathit{\text{Process-based}}$ reconstructions to investigate the effect of a NCC on the equation of state (EOS) $w(z)$ of evolving dark energy (DE) component. We find that a NCC is slightly preferred in both the two reconstructions by up to $\simeq 1\sigma$. Although the degeneracy between the EOS of evolving DE component and NCC weakens the constraint on the reconstructed $w(z)$, this degeneracy leads to the phantom divide $w=-1$ more consistent with the 1$\sigma$ posterior of $w(z)$.