DESI Data Put Holographic Dark Energy Models to the Test

The universe is not just expanding; it is accelerating, and the mysterious component driving that acceleration—dark energy—remains one of the deepest puzzles in modern physics. In the standard cosmological model, known as Lambda-CDM, dark energy is a cosmological constant: a perfectly uniform vacuum energy that never changes over cosmic time. This simple picture has survived decades of observational scrutiny, from the cosmic microwave background to the clustering of galaxies. Yet it carries well-known theoretical wounds, including the cosmological constant problem and the coincidence problem, and it sits at the center of the so-called Hubble tension, a stubborn disagreement between the expansion rate measured in the early universe and the rate measured locally. Now, a new comparative study published in The European Physical Journal C has subjected three theoretically motivated alternatives—holographic dark energy, agegraphic dark energy, and Ricci dark energy—to the sharpest late-time observational test yet, using the latest baryon acoustic oscillation data from the Dark Energy Spectroscopic Instrument.

The research, carried out by Jiayuan Huang, Tonghua Liu, and Chenggang Shao of Yangtze University, is notable for its methodological discipline. Rather than fixing the sound horizon—the baryon drag ruler that underpins baryon acoustic oscillation measurements—to a value inferred from early-universe cosmic microwave background data, the team treated it as a free parameter. This choice means the analysis relies purely on late-time information: cosmic chronometer measurements of the Hubble parameter, three independent Type Ia supernova compilations (Pantheon+, DES-Dovekie, and DESY5), the DESI DR2 baryon acoustic oscillation dataset, and an extended compilation of redshift-space distortion measurements that probe the growth of cosmic structure. Five different data combinations were analyzed using Bayesian Markov chain Monte Carlo sampling, and the competing models were scored against Lambda-CDM with the Akaike and Bayesian information criteria.

The three models share a common intellectual ancestry in the holographic principle, a deep idea from quantum gravity suggesting that the information content of a region of space is bounded by its surface area, not its volume. In holographic dark energy, the vacuum energy density is capped by the mass of a black hole of the same size, producing a density proportional to the inverse square of an infrared cutoff length. The original version of the model, proposed by Miao Li in 2004, identifies that cutoff with the future event horizon of the universe, introducing a dimensionless parameter c that controls the dark energy’s equation of state. When c exceeds one, dark energy behaves like quintessence, a slowly evolving field; when c equals one, the model approaches a de Sitter state, indistinguishable at the background level from a cosmological constant; and when c falls below one, the dark energy becomes phantom-like, with an equation of state more negative than minus one.

The results for this flagship model are striking in their precision. Across all data combinations that include DESI DR2 baryon acoustic oscillations, the holographic parameter converges to values extremely close to unity, with the full dataset including redshift-space distortions yielding c = 1.011 with an uncertainty of about 0.07. The Hubble constant comes out at roughly 67.3 to 68.0 kilometers per second per megaparsec, and the matter density at about 0.27. Physically, this means the data are steering the model directly toward the de Sitter boundary—the razor’s edge between quintessence-like and phantom-like behavior—rather than into a robust phantom regime. In other words, the best-fitting holographic universe looks, at the level of its expansion history, remarkably like the standard cosmological constant it was designed to replace.

The agegraphic model takes a different route to the same holographic inspiration. Instead of a spatial horizon, it ties the dark energy density to the conformal age of the universe, drawing on spacetime quantum fluctuations and the Karolyhazy uncertainty relation. This construction makes the model unusually predictive: the matter density is not a free parameter at all but is fixed by the flatness condition and the normalization of the expansion rate once the Hubble constant and the model parameter n are specified. The analysis finds n stably pinned at about 2.78 to 2.81 across all baryon acoustic oscillation combinations, indicating that the data consistently select the same age scale for the onset of late-time acceleration. But this economy comes at a price. The model prefers a Hubble constant of only 66.5 to 66.8 kilometers per second per megaparsec, and the information criteria generally disfavor it relative to Lambda-CDM once DESI DR2 data are included, with the full dataset giving a difference of 3.51 in both criteria.

Ricci dark energy is the most radical of the three. It identifies the infrared cutoff with the Ricci scalar curvature of spacetime itself, linking the dark energy density directly to the Hubble parameter and its time derivative. This gives the model an analytical expansion history and considerable flexibility at the background level, and it shows: the Akaike criterion actually favors Ricci dark energy over Lambda-CDM in all baryon acoustic oscillation combinations, with differences reaching nearly ten units for the DESY5 supernova sample. The Ricci parameter gamma is tightly constrained at about 0.53 to 0.55. Yet this statistical success conceals a serious physical problem. The model persistently prefers a matter density of only 0.215 to 0.219—roughly nine sigma below the Planck 2018 value of 0.315. Because the curvature-linked dark energy can absorb part of the distance behavior normally attributed to matter, the model achieves its good fit by effectively hiding matter inside its dark energy component, a trade-off that clashes with early-universe and structure-formation expectations.

The growth of cosmic structure provides an independent cross-check, and here the picture becomes more nuanced. Redshift-space distortion measurements of the quantity f-sigma-8, drawn from surveys including 6dFGS, SDSS, WiggleZ, VIPERS, FastSound, and eBOSS, probe how fast matter fluctuations grow over cosmic time. When these data are added, the fitted present-day fluctuation amplitude sigma-8 comes out at 0.875 for holographic dark energy, 0.893 for agegraphic dark energy, and a notably high 0.961 for Ricci dark energy. The combination of low matter density and high fluctuation amplitude in the Ricci case is physically suggestive: with less matter in the background, a larger fluctuation amplitude is needed to match the observed growth data. The authors are careful to stress, however, that this is a phenomenological consistency check, not a full perturbative stability analysis. Whether Ricci dark energy is genuinely viable at the level of linear perturbations depends on the complete dynamical trajectory and remains an open question for future work.

One of the most consequential findings concerns the Hubble tension itself. Because baryon acoustic oscillation measurements constrain ratios of distances to the sound horizon, freeing that horizon induces a strong negative correlation with the inferred Hubble constant, with Pearson coefficients between roughly minus 0.93 and minus 0.97 across all models and data combinations. Yet the fitted sound horizon values remain close to the standard scale of about 147 megaparsecs, meaning none of the three holographic models resolves the tension by shrinking the baryon acoustic ruler. All three prefer Hubble constants in the 66.5 to 68 range—comfortably near the Planck value of 67.4 and far below the SH0ES local measurement of 73.04. The reconstructed equation-of-state evolution reinforces this conclusion: holographic dark energy stays above minus one with a present-day value near minus 0.9, agegraphic dark energy is quintessence-like by construction, and Ricci dark energy hovers near minus 0.8 today with rapid evolution at higher redshift. No model shows robust evidence of crossing the phantom divide.

The bottom line is a sobering but honest verdict on one of cosmology’s most elegant theoretical programs. Holographic dark energy emerges as the most balanced performer of the three, statistically competitive with Lambda-CDM by the Akaike criterion—though not decisively so once the Bayesian criterion penalizes its extra parameter—while agegraphic dark energy is disfavored and Ricci dark energy’s apparent success is undermined by its anomalously low matter density. The study also demonstrates the power of the DESI DR2 dataset to drive model parameters toward sharp, physically meaningful values rather than vague allowed ranges. As the authors note, the near-de Sitter solution preferred for holographic dark energy is increasingly degenerate with a cosmological constant at the background level, so the decisive test will come from perturbation-level observables: weak lensing, full-shape galaxy clustering, and the integrated Sachs-Wolfe effect. For now, the holographic idea survives, but the universe, as measured by our best instruments, still looks stubbornly like one governed by a simple constant.

Subject of Research: Observational constraints on holographic, agegraphic, and Ricci dark energy models using late-time cosmological data

Article Title: Late-time cosmological constraints on three holographic dark energy models with DESI DR2 BAO and Type Ia supernovae

Article References: Huang, J., Liu, T., & Shao, C. (2026). Late-time cosmological constraints on three holographic dark energy models with DESI DR2 BAO and Type Ia supernovae. The European Physical Journal C, 86(9), Article 1042. https://doi.org/10.1140/epjc/s10052-026-16300-z

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16300-z

Keywords: dark energy, holographic principle, DESI DR2, baryon acoustic oscillations, Type Ia supernovae, Hubble tension, cosmology, Lambda-CDM, cosmic chronometers, redshift-space distortions, phantom divide, Markov chain Monte Carlo