Smooth sign switch of dark energy: testing the ΛsCDM model ✛ ✦
Context
The standard cosmological model expansion of the Universe ΛCDM, based on Friedmann equations, faces growing tensions: cosmic microwave background (CMB) gives a different value of the Hubble constant than measurements by Adam Riess using supernovae, and the accelerated expansion discovered by Saul Perlmutter and Brian Schmidt points to possible dynamics of dark energy. DESI baryon acoustic oscillation data have strengthened the motivation to test phenomenological extensions where the cosmological constant changes sign in the past.
Methods
To test the model with a smooth transition, the authors used supernovae data from DES-SN5YR with Dovekie recalibration, 12 BAO measurements from DESI, and 7 data points for the growth of large-scale structure fσ8. Parameters were estimated via numerical Monte Carlo Markov chain using a vectorized solver for linear growth of perturbations in the sub-horizon approximation. All calculations relied on Friedmann equations for a flat Universe and the energy conservation law for the dark component.
Results
The analysis showed that the data do not favor the smooth switching model: the χ² value is nearly identical to ΛCDM (1656.15 vs. 1656.07). The transition redshift z† = 3.5 +1.0 -1.0 lies deep in the dark matter dominated epoch, and the smoothness parameter Δ = 24.75 +17.4 -17.5 is completely unconstrained and follows the prior distribution. Adding growth rate data from galaxy surveys did not improve the situation. Thus, the smoothness of the transition is indistinguishable, and the model does not statistically outperform standard ΛCDM.
Implications
This means that late-time geometric probes cannot detect a sign change of dark energy if it occurs at z > 2.5. To test such scenarios, cosmic microwave background data that pin down early physics, as well as gravitational lensing to monitor the growth of potentials, are critically needed. The model may be relevant for alleviating tensions in neutrino masses.
Future development
Future surveys such as LSST and Simons Observatory will improve precision by an order of magnitude: the projected uncertainty on z† will be ~0.11–0.18, and Δ could be measured with an accuracy of ~1–1.5, sufficient to distinguish a sharp phase transition from a smooth crossover. This opens the way to understanding the nature of dark energy.
Impact
The results are important for cosmology, dark energy physics, large-scale structure theory, and neutrino physics, as they touch upon fundamental questions about the vacuum of the Universe.
Next steps
The next step should be a joint analysis with full CMB (Planck, ACT), inclusion of weak lensing data, and updating to DESI DR2 to test whether the model can resolve the neutrino boundary tension.
Key open problems
The model is directly linked to unsolved problems: the nature of dark energy, the Hubble tension, the S8 discrepancy, and the boundary anomaly of neutrino masses, hinting at possible incompleteness of standard cosmology.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors compared a ΛsCDM model with a smooth sign-switching dark energy against ΛCDM, using DES-SN5YR supernova data, DESI BAO, and fσ8 measurements. The results show that the data cannot distinguish between the models: χ² is nearly identical, the smoothness parameter Δ is unconstrained, and the transition occurs at z > 2.5, beyond the sensitivity of late-time geometric probes.
Where its strength is
This work demonstrates that a smooth dark energy transition cannot be distinguished from ΛCDM with current data, setting clear boundaries for phenomenological models and highlighting the need for early-time probes.
Where it could go next
- It might be interesting to see how including cosmic microwave background data affects constraints on transition parameters, especially z† and Δ, since the paper emphasizes their critical role.based on: The Breath of the Universe: How Dark Energy's Sign Change Eases the Tension arXiv:2607.05044
- A nearby approach is microscopic modeling of dark energy as a scalar field, which could provide a physical motivation for the transition shape and predict its smoothness.based on: Dark-Sector Seesaw: How a Scalar Spring Solves Cosmological Puzzles arXiv:2607.27515v1
- It would be interesting to explore how a smooth transition affects structure growth and lensing, using methods developed in the work on dark energy bubbles, to test against future data.based on: Bubble in a Sea of Dark Energy arXiv:2607.18376v1
Worth trying
- Test how constraints change when adding Planck CMB data, especially for z† and Δ.
- Use predictions for fσ8 at z > 2.5 from future surveys to test the model.
- Consider the impact of a smooth transition on weak gravitational lensing.
Why this may matter
The study clarifies which observational data are necessary to test sign-switching dark energy models and could steer future efforts toward the early universe and structure growth.
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Original abstract
as written by the authors arXiv:2607.06735
Recent baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI), in combination with CMB and supernova data, show a mild preference for dynamical dark energy over flat $$\Lambda$$CDM. They can also drive the best-fit effective neutrino mass to unphysical negative values, motivating models that mimic this effect through late-time expansion physics. The sign-switching cosmological constant ($$\Lambda_s$$CDM) model addresses this by introducing an AdS-like negative vacuum energy density at high redshifts ($$z > z^\dagger$$) that transitions to a dS-like positive density at low redshifts. While original fits assumed a discontinuous step function transition, we generalise the dynamics using a smooth hyperbolic tangent parametrisation, $$\Lambda(z) \propto \tanh[\Delta(z^\dagger - z)]$$. We constrain the transition redshift $$z^\dagger$$ and smoothness parameter $$\Delta$$ using background distance data from DES-SN5YR (with Dovekie recalibration) and DESI 2024 BAO. We further incorporate a compact redshift space distortion (RSD) $$f\sigma_8$$ compilation. The joint data do not prefer the smooth sign-switching model over flat $$\Lambda$$CDM, yielding nearly identical $$\chi^2_{\text{min}}$$ values, while information criteria penalise the additional parameters. The transition smoothness remains unconstrained and dominated by the prior volume ($$\Delta = 24.75^{+17.42}_{-17.48}$$), indicating that current data cannot distinguish between a sharp transition and a smooth dynamical crossover. This work does not directly constrain the physical sum of neutrino masses $$\sum m_ u$$; rather, it shows that current late-time background and growth data alone cannot resolve the transition details. We discuss the implications of this null detection and present projections for next-generation surveys.
Interestingly, at the transition moment the dark energy density becomes zero and its equation of state 'blows up' to infinity — yet the pressure remains smooth and no singularity arises.
Key numbers
- transition redshift: 3.5 +1.0 -1.0
- transition smoothness: 24.75 +17.4 -17.5 (unconstrained)
- matter density parameter: 0.315 ± 0.014
- chi-squared for smooth model: 1656.15 (vs 1656.07 for ΛCDM)
- number of supernovae used: ~1800