Dark Energy with a Smooth Sign Change: A Solution to the Hubble Tension?
The ECDM model is studied — a variant of sign-changing dark energy where its density evolves from negative to positive. A consistent formalism of perturbation equations is developed, working correctly even when the equation of state parameter diverges. The model is confronted with data from Planck 2018, ACT DR6, SPT-3G, DESI DR2, Pantheon+ and SH0ES. Including perturbations allowed checking the impact on structure growth and cosmic microwave background anisotropies. Results show compatibility with precision observations and a softening of the Hubble tension. Such a scenario offers a compelling modification of the late-time dynamics of the universe.
Context
The discrepancy in the Hubble constant (H0) from cosmic microwave background observations (early Universe) and local measurements of Cepheids and supernovae (late Universe) with the Hubble Space Telescope has exceeded 5σ. In ΛCDM, dominated by dark matter and a cosmological constant, early Universe predictions give H0=67.4 km/s/Mpc, while local measurements calibrated by Vera Rubin's observations of galaxy rotation yield H0=73.0 km/s/Mpc. This tension, first noted by Edwin Hubble himself, challenges the standard model and calls for a revision of dark sector physics.
Methods
The authors constructed an ECDM model where dark energy density is described by an analytic error function, ensuring a continuous transition from negative values (anti-de Sitter phase) to positive ones (de Sitter phase) at redshift z†. To properly describe perturbation evolution when the equation of state diverges, a renormalized equation system was developed for the variable f = δ/(1+w). The analysis used Markov chain Monte Carlo with data from: cosmic microwave background (Planck, ACT, SPT), baryon acoustic oscillations (DESI DR2), and Type Ia supernovae (Pantheon+), calibrated to local H0 measurements. The model is based on the Friedmann–Lemaître–Robertson–Walker metric, proposed by Georges Lemaître, and includes primordial nucleosynthesis as a constraint on helium abundance.
Results
Joint analysis revealed two transition regimes: fast and slow, with the slow one excluded when adding supernova data. For the full dataset (CMB+DESI+PantheonPlus&SH0ES), the model yields H0 ≈ 69.3 km/s/Mpc (incorporating the speed of light in distance definitions), much closer to the local value and reducing the tension to 2–3σ. Meanwhile, the S8 parameter, describing the clustering of dark matter, remains consistent with ΛCDM. Importantly, the data reject an ultra-fast transition (η→∞), favoring a moderate speed, which suppresses the growth of structures on scales probed by the Hubble telescope. Statistical criteria (e.g., ΔWAIC ≈ −15) indicate a strong preference for ECDM over ΛCDM.
Implications
This study shows that dark energy might not be a constant but could have complex dynamics, including a sign change in energy density. Such behavior could have influenced the formation of large-scale structure, seen through spectroscopic surveys, and left an imprint on the lensing of the cosmic microwave background. The obtained constraints on the transition speed motivate the development of microphysical models, e.g., based on scalar fields, and change how we interpret data from space telescopes.
Future development
Future data from the Euclid mission and the Rubin Observatory will refine the growth of structure and test ECDM predictions, especially regarding dark matter and its interaction with dark energy. A shift from phenomenological descriptions to fundamental theories, such as modified gravity or quintessence, will also be needed to explain the origin of the sign change and its connection to quantum effects in the early Universe.
Impact
The results are important for cosmology, astrophysics, and particle physics, as they link the Hubble constant tension to the nature of the dark sector, influencing the interpretation of data from the Hubble telescope and future missions.
Next steps
Next steps include incorporating large-scale structure data such as weak lensing from DES, and constructing scalar realizations of the model free from numerical difficulties, for testing in the context of inflationary cosmology.
Key open problems
The model directly addresses unsolved problems in physics: the nature of dark energy (why the cosmological constant is so small), the coincidence of matter and dark energy densities in the present epoch, and the nature of dark matter. Sign-changing dark energy could be connected to the string theory landscape, where transitions between vacua with different energies are possible, and to quantum correlations in the multiverse.
🎯 In the ECDM model, dark energy was negative in the past, meaning it provided extra attraction that slowed the Universe's expansion even more than ordinary matter. It's like a temporary 'gravitational well' from which the Universe emerged 3–4 billion years ago. Such an episode could have left traces as anomalies in large-scale structure.
🎬 The concept of sign-changing dark energy recalls the 'flip' of physical laws described in Liu Cixin's 'Three-Body Problem' trilogy, where the Universe cycles through different dimensions, causing radical shifts in its dynamics. Dan Simmons' 'Hyperion' also features 'temporal fields' that alter the flow of time and the expansion of space.
Key numbers
- Hubble constant discrepancy in ΛCDM: ~6.3 km/s/Mpc, >5σ
- Hubble constant in ECDM (full dataset): 69.3 ± 0.4 km/s/Mpc
- Preferred transition redshift range: 2.5 < z† < 3.5
- WAIC improvement over ΛCDM: ΔWAIC ≈ -15 (strong preference)