Hubble Tension in k-essence: Evidence for Robust Alleviation ✦
The Hubble tension is one of the most significant discrepancies in the standard ΛCDM cosmological model. K-essence models, which include non-trivial self-interactions of dark energy, can alter the background expansion after recombination, affecting the sound horizon calculation and thus the inferred Hubble constant. This study analyzed two physically motivated models — dilaton and tachyon — using data from Planck and five late-universe surveys: Pantheon+SH0ES, a set of cosmic chronometers (CC), the Union3 compilation, DES Y5, and DESI. For ΛCDM, the tension is 5.89σ; in the dilaton and tachyon models, combining all late-time data reduces it to 0.14σ and 0.69σ, respectively. This reduction is stable for any combination of datasets and requires no parameter tuning: the model parameter values remain unchanged regardless of the datasets used. The results show that the Hubble tension is not an inevitable feature of the late Universe but critically depends on how dark energy is described.
Context
The Hubble tension is a statistically significant discrepancy between the values of the Hubble constant H0 measured from the cosmic microwave background (early Universe) and from local supernovae and other distance indicators (late Universe). In the standard ΛCDM cosmological model, based on dark energy, dark matter and general relativity, this discrepancy exceeds 5σ, suggesting possible incompleteness of the model. According to Hubble's law, discovered by Edwin Hubble, local expansion linearly relates velocity and distance, while global dynamics are dictated by the Friedmann equations. Resolving this contradiction is crucial for understanding the nature of dark energy and the expansion of the Universe.
Methods
The authors used the Markov Chain Monte Carlo (MCMC) method to determine parameters in two physically motivated k-essence models—dilaton condensate and tachyon field. The analysis includes data from the Planck satellite's cosmic microwave background (reduced parameter set: acoustic scale, shift parameter, and baryon density), as well as several compilations of late-time observations: Pantheon+SH0ES (calibrated with Cepheids, Adam Riess et al.), Union3, DESY5 supernova data and DESI baryon acoustic oscillations, plus cosmic chronometers. For supernovae in the Hubble flow, the theoretical apparent magnitude was computed via the distance modulus, which includes the speed of light as a fundamental constant. The direct tension test was implemented by independently deriving constraints on H0 from early (Planck) and late (all combinations) data in each model, then calculating the discrepancy.
Results
In ΛCDM, the tension between Planck and Pantheon+SH0ES was 5.31σ (H0 = 67.27±0.60 and 73.37±0.98 km/s/Mpc). In the dilaton model it decreased to 2.64σ, and in the tachyon model to 1.58σ. With the inclusion of other late-time datasets (Union3, DESY5, DESI, cosmic chronometers), the qualitative picture persisted: in all combinations the k-essence models showed less tension than ΛCDM. The most comprehensive combined dataset (all late-time probes) gave a discrepancy with Planck of just 0.14σ for the dilaton and 0.69σ for the tachyon model, whereas ΛCDM showed 5.89σ. Importantly, the parameters of the k-essence models themselves remained stable when switching from one dataset to another, indicating an intrinsic rather than fine-tuned nature of the tension alleviation.
Implications
The results imply that the observed Hubble tension may be an artifact of assuming a cosmological constant as the form of dark energy, and that more general models with a dynamic equation of state can naturally reconcile early and late measurements. This echoes the early ideas of Georges Lemaître about possible variability of the cosmological constant and encourages a reassessment of the status of ΛCDM.
Future development
Future work must check whether the agreement holds when including other early data, such as WMAP, ACT, and SPT, since only Planck was used here as the currently most precise instrument. Furthermore, an important step will be comparison with observational constraints on the growth of structure to ensure that k-essence models do not violate the known evolution of large-scale structure.
Impact
The work will influence the interpretation of data from ongoing and planned surveys (Euclid, Roman Space Telescope), as well as theoretical constructions in the field of dark energy and modified gravity.
Next steps
Immediate next steps include testing the sensitivity of the results to the choice of prior parameter distributions, and a full joint analysis with weak lensing and galaxy cluster data to simultaneously resolve both the Hubble tension and the σ8 tension.
Key open problems
The research directly addresses the problem of the nature of dark energy and accelerated expansion, as well as the question of whether the cosmological constant is the final answer or merely an approximation. The reduction of the Hubble tension in k-essence models allows preserving dark matter and the overall ΛCDM structure, modifying only the dark energy sector, which could point the way to a deeper theory.
🎯 Interestingly, the idea of k-essence—a scalar field with a non-canonical kinetic term—originally emerged in the context of inflationary cosmology and was only later rediscovered as a dark energy model. The name 'k-essence' itself comes from 'kinetic quintessence'.
🎬 The tachyon field in cosmology vaguely resembles the fictional tachyons from 'Star Trek'—particles that move faster than light. However, here the tachyon is a scalar field with unconventional dynamics that does not violate causality.
Key numbers
- H0 Planck: 67.4 km/s/Mpc
- H0 SH0ES: 73.0 km/s/Mpc
- Tension ΛCDM: 5.3σ
- Tension dilaton: 2.6σ
- Tension tachyon: 1.6σ