Preprint reports >3σ evidence for w = −1 ‘phantom crossing’ in CPL dark‑energy fits

A new arXiv preprint from researchers at the University of Texas at Dallas argues that a statistical technique called an “optimal redshift” analysis strengthens the case that dark energy, in one widely used model, crosses the key line at w = -1. In several combinations of current cosmology data, the signal rises above 3 sigma.

That matters because w = -1 is the value expected for a cosmological constant, the simplest standard description of dark energy, the unknown component thought to be driving the universe’s accelerated expansion. A robust crossing of that line would point beyond a simple cosmological constant and also beyond simple single-field quintessence models, which generally do not cross it.

The paper, “The optimal redshift for dark energy II: application to cosmological data and the evidence for the phantom crossing of the CPL equation of state,” was posted to arXiv on Aug. 26. It was written by Travis Seth Rippentrop, Mustapha Ishak and Kristian Gonzalez of UT Dallas’ physics department.

The study applies an “optimal redshift” framework introduced in a companion paper to combinations of baryon acoustic oscillation data, cosmic microwave background measurements and Type Ia supernova data. The authors write in the abstract: “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.”

Within the CPL parameterization — a common two-parameter form written as w(a) = w0 + wa(1 − a) — the paper says some data combinations place the dark-energy equation of state below -1 before the crossing with sampled significance levels of 3.01 to 3.22 sigma. After the crossing, some combinations place it above -1 with sampled significance levels of 3.30 to 3.55 sigma.

The distinction matters. The paper is not claiming 3.55 sigma evidence for phantom dark energy across the board. Its strongest result on the “phantom” side, where w is below -1, is 3.22 sigma. The larger figures refer to the other side of the crossing, where w is above -1.

Among the examples highlighted in the paper’s Table III, a combination of DESI Data Release 2 baryon acoustic oscillation data and CMB data gives a sampled optimal-redshift tension of about 3.01 sigma, with the optimal value below -1. A combination of DESI DR2, Dark Energy Survey Year 6 BAO, CMB and South Pole Telescope power-spectrum data reaches 3.22 sigma, again below -1. On the other side of the crossing, a combination of DESI DR2, DES Y6, the recalibrated Dovekie supernova set and CMB data reaches 3.55 sigma, with the optimal value above -1.

Overall, the authors say they ran Markov chain Monte Carlo analyses for 15 dataset combinations. The data used include DESI DR2 BAO, DES Y6 BAO with overlap removed to keep it independent of DESI, Planck Data Release 3 plus Atacama Cosmology Telescope lensing, some combinations using South Pole Telescope data, and several supernova compilations including DES Year 5, Union3, Pantheon+ and recalibrated variants such as Dovekie, Union3.1 and PP_Hoyt.

The paper also distinguishes between Gaussian-derived and MCMC-sampled significance estimates because the statistical posteriors can be non-Gaussian. The authors emphasize the sampled values as the more relevant measure for their main claim.

The biggest caveat is that the result is model-dependent. It is specific to CPL, a standard but simplified way of describing a changing dark-energy equation of state. Other researchers have argued that restricting analyses to CPL can change the apparent significance of a signal, and in some cases can make “phantom crossing” behavior look stronger or cleaner than it would in a more flexible description of cosmic history.

The authors make that limitation explicit. “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,” they write.

The preprint lands in an active debate that intensified after DESI DR2 and follow-up studies in 2025 and 2026 raised fresh questions about whether dark energy may be evolving rather than constant. For now, the UT Dallas paper offers a new statistical framing of existing data — one that, within CPL, pushes several crossing results past 3 sigma, but stops short of settling what dark energy really is.