A combined DESI Full-Shape fit suggests that the inferred matter-density parameter may rise with redshift. The signal is positive but modest: the fitted trend sits 1.8 standard deviations from a model in which the matter-density parameter stays constant. Current statistical comparisons do not make that result decisive.
The study is a modelling analysis of previously reported DESI Full-Shape constraints. It fits a redshift-dependent line to the matter-density parameter and compares it with a constant-Ωm model using the same constraints. The central question is whether the added slope is supported by the data strongly enough to justify the more flexible description.
A small rise across a broad redshift range
The input combined six earlier DESI DR1 Full-Shape constraints from non-Lyman-alpha tracers with one DESI DR2 Lyman-alpha constraint. The DR1 measurements covered effective redshifts from 0.295 to 1.491, while the DR2 Lyman-alpha point was at an effective redshift of 2.33. The constraints were compared as a function of redshift, the variable used in the fitted trend.
The changing model treats the matter-density parameter, written as Ωm, as a straight line with redshift: it has a starting level plus a slope multiplied by redshift. The fit returned a slope of 0.022 with an uncertainty of 0.012. In plain terms, the estimated matter density increases across the redshift range in the combined fit, although the uncertainty and model comparisons leave a constant value plausible.
The line reduced the minimum chi-square by 3.5, a measure of the mismatch between a model and the data, but the information-criterion tests did not clearly separate the two descriptions. The change in AIC was -1.4 and the change in the small-sample AICc was 0.7. The authors judged models with differences of this size statistically indistinguishable.
A second model comparison reached much the same broad conclusion. The Bayesian evidence ratio for the line model against the constant model was B10=1.5. That amounts to only a weak preference for the line and does not strongly separate the two models.
What the trend would mean for dark energy
The authors then translated the fitted trend into common dark-energy parameterisations. In the simpler wCDM model, the dark-energy equation-of-state parameter was below -1 at a reported significance of 1.7 standard deviations. Values below -1 are described in this framework as the phantom regime. But in the broader w0waCDM parameter space, the standard Lambda-CDM case was recovered within 1 standard deviation.
The same diagnostic links the direction of the matter-density trend to different dark-energy regimes: an increasing Ωm(z) trend maps to w(z) below -1, while a decreasing trend maps to w(z) above -1. In a related hierarchy discussed in the preprint, a decrease followed by an increase is interpreted as a transition from the quintessence regime to the phantom regime. These mappings are model-dependent and do not by themselves establish a physical transition.
The reported 68% credible intervals show why the interpretation depends on the chosen model. In wCDM, the matter-density parameter was 0.325 with bounds of +0.016 and -0.017, while the constant equation-of-state value was -1.130 with bounds of +0.075 and -0.081. In w0waCDM, the corresponding matter-density estimate was 0.336 with bounds of +0.019 and -0.026, the w0 value was -1.04 with bounds of +0.17 and -0.14, and the wa value was -0.8 with bounds of +1.2 and -1.3.
A stronger test depends on what future data do
The preprint asks what might happen if future DESI measurements became more precise while their central values stayed where they are now. Under that simplified forecast, the fitted slope remained 0.022 but its uncertainty narrowed to 0.011, giving a reported 2-standard-deviation significance. The forecast statistics weakly favoured the line model: the change in minimum chi-square was -4.8, the change in AIC was -2.8, the change in AICc was -0.6, and the Bayesian evidence ratio was 2.2.
The study also used simulated forecast mocks to show the range of possible outcomes. In that forecast, the slope significance was 2.1 with an uncertainty of 0.6 standard deviations. Forty percent of the simulated cases had a Bayesian evidence ratio above 3, and 14% rose above 10, thresholds the analysis labels as moderate and strong evidence on its chosen scale.
A final-release scenario projected a slope significance of 2.9 with an uncertainty of 1.0 standard deviation. In that scenario, 70% of simulated cases exceeded a Bayesian evidence ratio of 3 and 53% exceeded 10. This is a forecast rather than a measurement from a completed DESI release, and it depends on the assumed future trend and error reductions.
Why the result is not yet a discovery
The central caution is that the analysis uses one Full-Shape observable. The authors say that this cannot by itself rule out a systematic explanation. The apparent trend therefore remains open to the possibility that it reflects systematics rather than a change in the underlying model.
The current model comparisons leave the main question open. The observed data show a positive fitted slope, but AIC, AICc and Bayesian evidence do not strongly distinguish the changing and constant descriptions. The dark-energy reading also depends on the selected wCDM or w0waCDM parameterisation, while the forecast depends on assumptions about future central values and errors.
The document is an arXiv version 2 preprint. Its forecast is best understood as a proposal for a future test: the present model comparisons do not amount to conclusive evidence for the line model.
Paper data and sources
Original title: A Prediction for DESI Full-Shape: Increasing Tomographic $Ω_m(z)$ Trend
Authors: Eoin Ó Colgáin, M. M. Sheikh-Jabbari
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text