The size of our cosmic horizon sets how much dark energy there is.
Holographic Dark Energy
Dark energy whose density is fixed by the size of the cosmic event horizon, following a holographic limit on what a region can contain.
Placeholder for a 3D visualisation of Dark Energy Candidates. The interactive scene will land in Phase 3. Roughly 69% of the universe's energy density drives accelerating expansion. Plain ΛCDM models it as a cosmological constant with equation of state w fixed at -1. This family asks what dark energy is as a physical substance, not how to parameterize it. The leading physical candidate is quintessence, a dynamical scalar field with w greater than -1 that evolves over cosmic time; phantom energy is its mirror image with w less than -1. Other candidates change the field's kinetic energy (k-essence), couple it to matter (coupled quintessence), tie its density to the cosmic horizon (holographic dark energy), or merge it with dark matter into one fluid (the Chaplygin gas, ruled out in its unified form). DESI's 2024 hint of evolving dark energy (w0 greater than -1, wa less than 0) is exactly the signature a physical field would leave, which is why these models are an active frontier rather than a settled question.
§1 · The claim, in one sentence
Holographic dark energy ties the dark energy density to the size of the cosmic event horizon, motivated by a limit from black hole physics on the entropy a region of space can hold.
§2 · Why it might be true
Bekenstein proposed a bound on the entropy of a region that grows with its area, more slowly than its volume. Cohen, Kaplan, and Nelson argued in 1999 that this bound ties a field theory's highest usable energy to the region's size.
Hsu noted in 2004 that such bounds can bring the vacuum energy down to the observed dark energy density. In his version, though, it has w = 0 and behaves like matter, which data strongly disfavour.
Miao Li proposed in 2004 to use the future event horizon as the size that sets the bound. This horizon marks the most distant events happening now that we could ever see.
For a dark energy fraction of 0.73, his model gave an equation of state of -0.90 today. He argued that inflation lasting the minimum number of e-folds also explains why dark energy dominates now.
The family stance
Dark energy may not be a constant. If its equation of state differs from -1, or changes with time, a cosmological constant cannot be the whole story and a dynamical component, most naturally a scalar field, is required. The case that the universe accelerates is overwhelming; the case for any one physical model of what drives it is not.
§2.5 · Evidence
- Early supernova fits matched the model, giving an equation of state of about -0.91 today with the free parameter set to 1 (Huang and Gong 2004).
- With DESI 2024 BAO and supernova data, the parametrization studied by Li et al. (2025) is statistically as viable as ΛCDM by Bayesian evidence.
- The model derives the dark energy scale from the holographic principle and dimensional analysis, leaving one free parameter.
§3 · What you'd need to test it
- An equation of state of about -0.90 today, for a dark energy fraction of 0.73 in the original model.
- For some values of its free parameter, the equation of state crosses -1 and turns phantom, a quintom-type behaviour.
- If the equation of state ends below -1, the expansion runs toward a Big Rip in the far future.
§4 · Where it breaks
- Adding cosmic microwave background data drives the fit to c below 1, with w crossing -1 at more than 10 sigma, and makes the model significantly less favoured than ΛCDM (Li et al. 2025).
- Zhang and Wu (2005) found that simulated supernova data built from a pure cosmological constant still pushed the model into its phantom-crossing range.
- A phantom future ending in a Big Rip is a problem shared with phantom energy, and interacting versions of the model are studied partly to avoid it.
Go deeper
Cohen, Kaplan, and Nelson (1999) start from Bekenstein's bound S < pi M_P^2 L^2 on the total entropy in a volume L^3. Because this scaling is non-extensive, they propose a relation between the UV and IR cutoffs of an effective field theory, so that local field theory stays valid where it has been tested. They discuss the consequences for the cosmological constant problem. Hsu (2004) showed that such entropy bounds make quantum corrections to Lambda finite and of order the observed 10^-10 eV^4, but with w = 0 on cosmological scales in those scenarios.
Li (2004) took the future event horizon as the IR cutoff. With Omega_Lambda = 0.73 he found w = -0.90 today, and argued that inflation with the minimal number of e-folds resolves the coincidence problem. The model's free parameter (c in Zhang and Wu, d in Huang and Gong) controls the late-time behaviour. Huang and Gong (2004) found w0 = -0.91 for d = 1, and a phantom-like w0 = -2.67 with d free. Zhang and Wu (2005) found that supernova fits favour c below 1, a quintom-type dark energy crossing w = -1, and that joint SNe, CMB, and LSS fits gave c = 0.81 and w0 = -1.03.
Li et al. (2025) refit the model and an interacting version to DESI 2024 BAO, CMB, and supernova data. Without CMB data, the interacting version keeps w above -1 at 1 sigma, and both match ΛCDM on Bayesian evidence. With CMB data, the plain model crosses w = -1 at beyond 10 sigma, and both fall significantly behind ΛCDM. Wang, Wang, and Li (2017) review the model, its constraints, its interacting versions and the big rip question. The holographic principle itself is covered in the Holographic Spacetime variant (Chapter 3), and the Big Rip in the Rip Scenarios family (Chapter 7).
▸§5 · Who built it, and when(7 sources, 7 established)
- EstablishedLi (2004). 'A Model of holographic dark energy.' Phys. Lett. B 603, 1
- EstablishedCohen et al. (1999). 'Effective field theory, black holes, and the cosmological constant.' Phys. Rev. Lett. 82, 4971
- EstablishedHsu (2004). 'Entropy bounds and dark energy.' Phys. Lett. B 594, 13
- EstablishedHuang & Gong (2004). 'Supernova constraints on a holographic dark energy model.' JCAP 08, 006
- EstablishedZhang & Wu (2005). 'Constraints on holographic dark energy from Type Ia supernova observations.' Phys. Rev. D 72, 043524
- EstablishedWang et al. (2017). 'Holographic Dark Energy.' Phys. Rept. 696, 1
- EstablishedLi et al. (2025). 'Revisiting holographic dark energy after DESI 2024.' Eur. Phys. J. C 85, 608
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