The cosmological parameter w — the ratio of dark energy pressure to its density — is like a signpost on a mountain pass: values above –1 correspond to quintessence, below –1 to phantom energy with a catastrophic future. Recent data from the DESI observatory, which has mapped millions of galaxies, hint that the Universe is not just accelerating but may have recently crossed this watershed. If that is the case, standard models of dark energy run into serious trouble. In general relativity, spacetime curvature is dictated by matter, and the expansion of the Universe determines the horizon's fate. A paper by Ukrainian physicist D. A. Yerokhin offers an elegant explanation: the cause may be not the energy itself, but the event horizon entropy, which obeys modified laws.
The model is based on the holographic principle: the physics of a volume is encoded on its boundary. For an expanding Universe, this boundary is the future event horizon — the greatest distance light will ever travel. The dark energy density is expressed through the entropy of the horizon, which is generalized: instead of the classic Jacob Bekenstein–Stephen Hawking entropy formula S ~ L², a function F(L) with quantum corrections by Barrow and Tsallis is introduced. The key ingredient is the local logarithmic slope χ = d ln F / d ln L, which controls the dynamics. Setting a scale‑dependent Barrow parameter, the author reconstructs the explicit F(L) and obtains a closed system of background equations.
The analysis reveals that the phantom divide is crossed on the 'kinematic branch' when HL = 1. Geometrically, this means the event horizon radius L attains a strict local maximum, with its derivative vanishing. That moment of a frozen horizon is the summit of the pass. The crossing direction depends on the local entropy dimension dS = 2 + χ. If dS < 4 (entropy grows slower than L⁴), the Universe slides from quintessence into the phantom regime. At the transition point dS = 4 + 3 w'/(1+q), where q is the deceleration parameter. From the measured slope of w with redshift one can directly probe horizon properties. An example with realistic parameters gives a future crossing (z ≈ –0.14) with dS ≈ 1.62. In the range 0 < ΩX < 1 such a transition is unique.
The result turns cosmological data into a test of gravity at Planck scales. If observatories confirm that w crosses –1 at z ~ 0.4–0.5 with a positive local $w_a$, then the entropy dimension turns out to be less than 3 — exactly as in Barrow's fractal horizon model. A negative $w_a$ is excluded. At the pass summit, the second law of thermodynamics is violated without additional dark energy entropy, and the standard perturbation theory breaks down. The phantom divide is a window into physics beyond the Standard Model.
The model can be extended to account for inhomogeneities. Non-adiabatic perturbations or additional fields will be needed to avoid a sound‑speed singularity. Further simulations and comparison with supernova and cosmic microwave background data will help calibrate F(L).
The work impacts our understanding of dark energy’s nature, horizon theory, and quantum gravity, bridging the macroscopic and microscopic worlds.
Direct comparison of the model with DESI DR2, Planck, and Pantheon+ data, and the construction of a regular perturbation theory.
The model touches on the cosmological constant problem, the nature of dark energy, and the ultimate fate of the Universe (including a possible Big Rip singularity), as well as the quantum structure of spacetime.
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
This work builds a model of dark energy where the density is set by the entropy of the future event horizon, with quantum corrections from Barrow and Tsallis. A local logarithmic slope χ is introduced, and it is shown that the crossing of the phantom divide (w = -1) occurs when the derivative of the horizon radius vanishes, i.e., when HL = 1. Using realistic parameters, a transition in the future (z ≈ -0.14) is obtained, along with a connection between the slope w and the entropy dimension.
Where its strength is
A direct geometric link is established between the phantom divide crossing and the extremum of the event horizon, turning cosmological data into a test of quantum-gravity corrections to entropy.
Where it could go next
Worth trying
Nearby works in our archive
The closest work in the archive sits at 0.68 by meaning — the usual level for our corpus.
At the transition point, the horizon entropy is maximal and the dark energy density is minimal — it’s as if the Universe lets out a sigh before a powerful tug.
The Big Rip scenario, in which accelerating expansion tears everything apart, appears in Charles Stross’s novel ‘Accelerando’.