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arXiv · 2608.25278

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

Travis Seth Rippentrop·Mustapha Ishak·Kristian Gonzalez
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Abstract

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 $3.01$--$3.22σ$ before the crossing point, and $3.30$--$3.55σ$ 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.

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Travis Seth Rippentrop, Mustapha Ishak, Kristian Gonzalez. 2026-08-26. The optimal redshift for dark energy II: application to cosmological data and the evidence for the phantom crossing of the CPL equation of state. https://arxiv.org/abs/2608.25278

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