Kristian Gonzalez | Searcharxiv

arXiv2026

The optimal redshift for dark energy II: application to cosmological data and the evidence for the phantom crossing of the CPL equation of state

Recent results from DESI and other cosmological datasets have indicated a preference for dynamical dark energy, with a time-evolving equation of state (EOS), $w(z)$. Furthermore, analyses using the CPL parameterization give an EOS with a phantom crossing of the $w(z)=-1$ line. In a companion paper-I, we assumed the CPL parameterization and its generalization, and introduced the formalism of the optimal scale factor (or redshift), a quantity designed to simultaneously maximize the distance from the cosmological constant value of $-1$ and to minimize the uncertainty on the EOS, thereby maximizing the tension with the cosmological constant at that specific redshift for a given dataset combination. In this paper-II, we apply the optimal-redshift formalism to available baryon acoustic oscillation, Cosmic Microwave Background, and supernova dataset combinations, with a particular focus on the phantom-line crossing within CPL. Motivated by the relatively low significance of previous constraints on the EOS in the region below the phantom line, we calculate the optimal redshift for a variety of dataset combinations to identify those that best constrain departures from $w(z)=-1$ before and after the crossing. We find combinations and corresponding optimal redshifts for which $w(z)$ lies below the ``$-1$'' line with new significance levels reaching $3.01$--$3.22\sigma$ before the crossing point, and $3.30$--$3.55\sigma$ above ``$-1$" after the crossing. Our focus in this work is the application of a new framework that maximizes the significance of the phantom-crossing signal within CPL using currently available datasets. Determining whether this crossing is effective or intrinsic, and identifying the underlying microphysical models, constitute separate questions from the aim of the present work and remain important directions for future investigation, further motivated by our findings. Abridged.

astro-ph.CO↗

arXiv2026

The optimal redshift for dark energy I: formalism and interpretation

We introduce the concept of the optimal redshift for dark energy, a statistically motivated redshift at which departures of the dark-energy equation of state (EOS) from the cosmological-constant value are tested most effectively. Within a generalized CPL parameterization, we derive an analytic expression for the optimal redshift by maximizing the separation of the EOS from $w=-1$ relative to the corresponding uncertainty. We establish the optimal redshift relationship to the phantom-crossing and pivot redshifts. As an illustration, we apply the formalism to the dataset combination of DESI DR2 BAO measurements, the DES Year-6 independent BAO measurement, and the recalibrated DES-Dovekie supernova sample. Adopting the null hypothesis $\mathcal{H}_0:w(a_{\rm opt})=-1$, we find a tension of ~$2.8\sigma$ with the cosmological-constant prediction at the optimal redshift, compared with ~$2.6\sigma$ at the pivot redshift, despite the latter having a smaller EOS uncertainty. This behavior reflects the specific design of the optimal redshift to maximize the statistical significance of a departure of the EOS from the -1 value of the $\Lambda$CDM model. We further provide statistical and geometrical interpretations of the optimum. In the CPL parameter space, the pivot corresponds to the projection that minimizes the variance of the equation of state, whereas the optimum maximizes its squared-distance from the cosmological-constant value over its variance. While the optimum is dataset and parameterization dependent, the underlying optimization principle and definition of the optimal redshift can be extended beyond the CPL framework. Future applications to DESI, Rubin LSST, Euclid, Roman Space Telescope, and other Stage-IV dark-energy surveys appear particularly promising.

astro-ph.CO↗