Constraints on Redshift-Binned Dark Energy using DESI BAO Data

We parameterize the equation of state of late-time dark energy as $w_{\mathrm{bin}}(z)$, with three redshift bins, characterized by a constant equation of state in each bin. Then, we constrain the parameters of the $w_{\mathrm{bin}}$CDM model using datasets from DESI BAO data, Planck CMB power spectrum, ACT DR6 lensing power spectrum, and type Ia supernova distance-redshift data of Pantheon Plus/DES Y5/Union3. The significances for $w_1>-1$ is $1.9\sigma$, $2.6\sigma$ and $3.3\sigma$, and $w_2$ is consistent with $-1$ within $1\sigma$ level, while $1.6\sigma$, $1.5\sigma$ and $1.5\sigma$ for $w_3<-1$ in these three data combinations with different choices of type Ia supernova datasets, respectively. Additionally, to alleviate $H_0$ tension, we incorporate the early dark energy (EDE) model in the early-time universe and add the SH0ES absolute magnitude $M_b$ prior (or $H_0$ prior) to further constrain the $w_{\mathrm{bin}}$EDE model. In the $w_{\mathrm{bin}}$EDE model, we find a $w_{\mathrm{bin}}(z)$ pattern similar to that in the $w_{\mathrm{bin}}$CDM model. The results of the three data combinations exhibit $w_1>-1$ at $1.9\sigma$, $1.7\sigma$ and $2.9\sigma$ level, meanwhile $w_3<-1$ at $1.3\sigma$, $1.3\sigma$ and $1.3\sigma$ level, respectively. In all, our results indicate that the transition of dark energy from phantom at high redshifts to quintessence at low redshifts is not conclusive.