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Observational constraints on Luciano-Saridakis holographic dark energy

This paper demonstrates that a generalized holographic dark energy model based on a new entropy framework is observationally viable, fitting current cosmological data as well as the standard $\Lambda$ CDM model while offering a theoretically motivated extension.

Original authors: Matías Leizerovich, Susana J. Landau, Giuseppe Gaetano Luciano, Andreas Papatriantafyllou, Emmanuel N. Saridakis

Published 2026-09-04

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CC BY 4.0

Original authors: Matías Leizerovich, Susana J. Landau, Giuseppe Gaetano Luciano, Andreas Papatriantafyllou, Emmanuel N. Saridakis

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, astronomers have watched the universe expand, but the story of how that expansion behaves has a stubborn gap in the middle. We know the cosmos is not just growing; it is speeding up, a phenomenon driven by a mysterious force called dark energy. The simplest explanation for this acceleration is a cosmological constant, a steady, unchanging energy inherent to space itself. This idea fits the math of our current best theories, yet it leaves physicists uneasy. The theoretical value for this energy is wildly different from what we actually observe, a discrepancy so large it suggests our understanding of the universe's fundamental rules might be incomplete. Because of this, scientists have spent years looking for alternatives, searching for a model that explains the acceleration without relying on a static, unchanging constant.

One promising avenue for this search comes from a concept called the holographic principle. This idea suggests that the information describing a volume of space is actually stored on its boundary, much like a three-dimensional object is encoded on a two-dimensional surface. When applied to the universe, this principle links the amount of dark energy to the size of the observable universe. However, the standard version of this theory has its own limitations. Recently, researchers proposed a more flexible version based on a new way of counting the microscopic states of the universe, using a mathematical framework that allows for two distinct types of entropy, or disorder, to exist simultaneously. This new model, known as the Luciano-Saridakis holographic dark energy scenario, offers a way for dark energy to evolve dynamically rather than staying fixed, potentially solving the tension between theory and observation.

In a recent study, a team of cosmologists put this new two-parameter model to the test against the most precise astronomical data available. They did not rely on a single type of measurement but instead combined four independent lines of evidence that probe the history of the universe's expansion. First, they looked at "cosmic chronometers," which are specific types of aging galaxies that allow astronomers to measure the expansion rate directly. Second, they analyzed data from thousands of exploding stars, known as Type Ia supernovae, which serve as standard candles to measure vast cosmic distances. Third, they examined the distribution of galaxies imprinted with sound waves from the early universe, a feature called baryon acoustic oscillations. Finally, they incorporated compressed information from the cosmic microwave background, the faint afterglow of the Big Bang, to anchor their models to the universe's earliest moments.

The researchers used these datasets to see if the new holographic model could fit the observations better than the standard, unchanging cosmological constant. They found that the new model works remarkably well. It successfully accommodates all the different datasets at once, a feat that the standard model struggles to achieve when trying to reconcile the expansion rate measured by early-universe data with that measured by nearby supernovae. The analysis revealed that the universe's expansion history is consistent with this new, more complex form of dark energy. The model allows for a dynamic evolution where the dark energy density changes over time, yet it naturally settles into a behavior that looks very much like the standard cosmological constant in the current era.

When the team compared the full two-part model against a simpler version that only uses one of the entropy contributions, the results were striking. Both versions described the data with nearly identical accuracy. The statistical evidence did not strongly favor the more complex, two-part version over the simpler one, suggesting that while the universe could be governed by this richer, dual-entropy structure, the current data does not yet demand it. The preferred values for the model's parameters place the universe very close to the standard cosmological constant limit, but they leave a small, viable window open for the new, more complex physics to be at work.

The study also provided a specific measurement for the current expansion rate of the universe, known as the Hubble constant. The new model yielded a value of 71.42 kilometers per second per megaparsec. This number sits comfortably between the lower value derived from the early universe and the higher value measured from nearby stars, effectively bridging the gap that has long troubled cosmologists. While the data does not prove that the universe is governed by this new two-parameter entropy, it demonstrates that such a framework is a viable and theoretically motivated alternative to the standard model. It offers a path forward where the mysterious acceleration of the cosmos is not a static accident, but a dynamic consequence of the deep statistical rules governing the universe's microscopic structure.

Technical Summary: Observational Constraints on Luciano-Saridakis Holographic Dark Energy

Problem and Motivation
The standard cosmological paradigm attributes the late-time accelerated expansion of the Universe to a cosmological constant ( $\Lambda$ ). While empirically successful, this interpretation faces significant conceptual challenges, most notably the vacuum energy discrepancy and the possibility that cosmic acceleration is a dynamical rather than static process. Holographic Dark Energy (HDE) offers an alternative framework based on the holographic principle, linking the vacuum energy density to a characteristic cosmological length scale.

Recent developments have introduced a two-parameter generalized entropic functional derived from a revised statistical framework and microstate counting, distinct from previous phenomenological deformations of the area law. This functional, characterized by two independent exponents, leads to a generalized holographic scaling for bounded systems. When integrated into a holographic framework, this results in an extended HDE scenario where the dark energy density comprises two independent holographic contributions. While the background cosmological implications of this framework have been theoretically explored, its observational viability and constraints against current cosmological data had not yet been assessed. This work addresses that gap by performing a rigorous observational study of the Luciano-Saridakis HDE scenario.

Methodology
The authors investigate the observational viability of the extended HDE model using a spatially flat Friedmann-Robertson-Walker background. The dark energy density is derived from the generalized entropy $S_{\delta,\epsilon} = \gamma_\delta A^\delta + \gamma_\epsilon A^\epsilon$ , leading to a modified density $\rho_{DE} = \gamma_\delta H^{2(2-\delta)} + \gamma_\epsilon H^{2(2-\epsilon)}$ under the Hubble-horizon infrared cutoff ( $L=H^{-1}$ ).

To constrain the model, the authors employ a comprehensive suite of observational probes:

Cosmic Chronometers (CC): Direct measurements of the Hubble parameter $H(z)$ from passively evolving galaxies.
Type Ia Supernovae (SNIa): The Pantheon++SH0ES compilation (1701 supernovae), incorporating Cepheid-calibrated low-redshift data.
Baryon Acoustic Oscillations (BAO): Constraints from the DESI DR2 dataset on the Hubble distance $D_H(z)$ and transverse comoving distance $D_M(z)$ .
Cosmic Microwave Background (CMB): Compressed shift parameters ( $R$ and $l_A$ ) derived from Planck 2018 data.

The analysis utilizes a Markov Chain Monte Carlo (MCMC) approach via the COBAYA framework combined with a modified CLASS Boltzmann solver. The parameter space includes the Hubble constant ( $h$ ), matter density ( $\omega_m$ ), baryon density ( $\omega_b$ ), and the model-specific parameters ( $\epsilon, \alpha_\epsilon, \alpha_\delta$ ). To mitigate strong degeneracies between parameters, the authors fix $\delta = 2$ for the primary analysis and also examine the reduced single-contribution limit where $\alpha_\delta = 0$ .

Key Contributions and Results
The study provides the first observational assessment of the Luciano-Saridakis cosmological framework. The joint analysis of all datasets yields the following key results:

Model Viability: The extended HDE model provides an excellent fit to the combined dataset. Crucially, it admits regions of parameter space where the Pantheon++SH0ES and Planck CMB constraints are simultaneously accommodated, a condition that proves problematic in a standard $\Lambda$ CDM joint analysis due to existing tensions.
Parameter Constraints:
- The preferred solutions lie close to the $\Lambda$ CDM regime. The entropic exponent is constrained to $\epsilon = 1.96^{+0.21}_{-0.23}$ (68% CL), which is compatible with the $\Lambda$ CDM limit of $\epsilon = 2$ .
- The amplitude $\alpha_\epsilon$ is consistent with zero within uncertainties, while $\alpha_\delta$ is constrained to $0.500^{+0.21}_{-0.056}$ (68% CL), indicating that the non-standard entropic contribution remains observationally viable but sub-dominant or degenerate with the standard limit.
- The inferred Hubble constant is $H_0 = 71.42 \pm 0.75$ km s $^{-1}$ Mpc $^{-1}$ , a value intermediate between the Planck $\Lambda$ CDM determination and the SH0ES local measurement.
- Standard cosmological parameters ( $\omega_m, \omega_b$ ) remain consistent with Planck $\Lambda$ CDM values within $2\sigma$ and $1\sigma$ , respectively.
Model Comparison (Full vs. Reduced): The authors compare the full two-sector model against the reduced single-contribution limit ( $\alpha_\delta = 0$ $α_{δ} = 0$ ).
- The minimum chi-square values are nearly identical ( $\Delta\chi^2 \approx 0.02$ ).
- Information criteria (AIC and BIC) indicate that the current data do not provide compelling statistical support for the additional parameter $\alpha_\delta$ . The BIC favors the reduced model more strongly, while the AIC suggests only a mild preference.
- Despite this, the extended scenario is fully compatible with observations, demonstrating that current data cannot distinguish between the single-sector and two-sector realizations.

Significance and Claims
The paper establishes generalized entropic HDE as a viable and theoretically motivated extension of the standard cosmological scenario. Its primary significance lies in demonstrating that this framework, rooted in generalized statistical mechanics and holographic entropy, can successfully reproduce the thermal history of the Universe and account for the transition to accelerated expansion while remaining consistent with current observational constraints.

The authors claim that while the data do not compellingly favor departures from $\Lambda$ CDM, the model offers a statistically acceptable alternative that naturally encompasses the standard cosmological constant as a limiting case. Furthermore, the framework's enlarged parameter space provides additional flexibility in accommodating different cosmological probes, potentially alleviating tensions between early- and late-time datasets (specifically between CMB and SNIa/SH0ES) without violating observational bounds. The work concludes that the Luciano-Saridakis framework successfully links microscopic entropic considerations to late-time cosmological observables, warranting further investigation into its potential to resolve persistent cosmological tensions.

Technical Summary: Observational Constraints on Luciano-Saridakis Holographic Dark Energy

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