A cosmology preprint reports evidence that the value used to describe dark energy falls below the benchmark w = −1 in one set of data and above it in another. The strongest pair of results reached 3.55 standard deviations above that line and 3.22 standard deviations below it, but the two findings came from different dataset combinations.
In this analysis, w is the equation-of-state quantity being compared with −1, the cosmological-constant value. The reported crossing is assessed within the CPL framework, a chosen mathematical form for how w changes with redshift, so it remains tied to that parameterization and the dataset combinations used.
A targeted search for the strongest departure
The study applies an optimal-redshift formalism to BAO, CMB and Type-Ia supernova combinations. The formalism seeks a redshift where uncertainty in w is reduced while its distance from the cosmological-constant value −1 is increased.
The researchers used Metropolis-Hastings Markov chain Monte Carlo sampling through Cobaya, with CAMB as the cosmological theory code. The analysis covered 15 different dataset combinations.
The workflow first fitted CPL to derive the optimal scale factor aopt and wopt from posterior means and covariance. It then fitted CPL* with a* fixed to aopt, and recorded sampled wopt. The one-dimensional null hypothesis was wopt = −1.
The data combinations did not all point the same way
The BAO+CMB combinations put wopt below −1, with values from −1.358 to −1.464. Their sampled tensions at the optimum ranged from 3.01 to 3.22 standard deviations; the upper end required SPT data.
Recalibrated BAO+SN+CMB triplets gave tensions of 3.30 to 3.55 standard deviations. The w0 values used for those tensions ranged from −0.812 to −0.737.
Across the fits, the predicted crossing redshift was about 0.50 for BAO+CMB, 0.35–0.45 for triplets and 0.44–0.51 for BAO+SN. These are ranges across combinations, not a single pooled uncertainty interval.
An alternative posterior-based tension measure raised maximum one-dimensional BAO+CMB tensions to 3.85–4.17 standard deviations. It is a different metric applied to the same posterior distributions, not an independent dataset result.
BAO+SN alone produced a more modest result after supernova recalibration: tensions of 2.47–2.76 standard deviations, with wopt between −0.859 and −0.906.
Why the crossing remains a model-dependent claim
Posterior contours from BAO+SN+CMB combinations showed no overlap with w = −1, except for DESI2+PP+CMB, and indicated stronger-than-3σ tension. BAO+CMB contours also showed an above-3σ preference for w < −1.
A caveat applies to the triplet figures. When aopt was greater than 1, the nominal optimum lay in the future, so the analysis used w0 rather than wopt in its plots and reported sampled values.
The two sides of the claimed pattern are therefore not measurements from one common observational sample: the below-line and above-line estimates come from different dataset combinations. The paper’s result is an inference within CPL and CPL*, not a model-independent physical crossing.
The tension figures should not be treated as interchangeable. The 3.01–3.22 values and the 3.85–4.17 values for BAO+CMB come from different ways of summarizing the same posterior information, while the triplet values use the future-optimum substitution described above.
An early result awaiting further tests
The supplied document is an arXiv version-one preprint dated 26 August 2026. It acknowledges Gemini assistance with plotting scripts and partial support from the Department of Energy Office of Science, award DE-SC0022184, and the National Science Foundation grant AST2327245.
Paper data and sources
Original title: The optimal redshift for dark energy II: application to cosmological data and the evidence for the phantom crossing of the CPL equation of state
Authors: Travis Seth Rippentrop, Mustapha Ishak, Kristian Gonzalez
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text