Not a thermodynamic story but a geometric one. The universe ends as empty, gently warm, curved space.
de Sitter Equilibrium
The geometric end state of eternal acceleration: the universe approaches empty de Sitter space, whose cosmological horizon carries a tiny temperature, and settles into equilibrium with its own horizon.
Looping ambient scene for Heat Death and Eternal Expansion. The current best-fit cosmology, ΛCDM, has dark energy driving an accelerating expansion that never reverses. Extrapolated forward, this is the default future of the universe: galaxies outside the Local Group recede beyond reach, star formation ends, stellar remnants cool, and over almost unimaginable timescales matter and even black holes decay away. The end state is a cold, dilute, near-empty space at maximum entropy, the heat death. This family collects the eternal-expansion futures that follow from a positive, roughly constant dark energy. The variants differ in emphasis: the thermodynamic timeline of decay, the geometric end state of an asymptotic de Sitter horizon, and the open question of what a dynamical (quintessence) dark energy does to the long-term picture.
§1 · The claim, in one sentence
de Sitter Equilibrium describes the same eternal-acceleration future in geometric rather than thermodynamic language. As matter and radiation dilute away, the universe approaches de Sitter space, the maximally symmetric solution for a positive cosmological constant. Gibbons and Hawking 1977 showed that the cosmological event horizon of such a space radiates at a fixed temperature, by analogy with black-hole radiation. The far future is then not a dead cold but a thermal equilibrium with the horizon, at a temperature near 10^-30 kelvin.
§2 · Why it might be true
A universe dominated by a positive cosmological constant does not just expand forever, it approaches a specific geometry: de Sitter space, the empty, maximally symmetric spacetime that a constant vacuum energy produces. As galaxies, light, and finally the last decay products thin out, the geometry left behind is essentially de Sitter, the same arena that drives inflation in the early universe, now reached as an end state instead of a beginning.
Gibbons and Hawking 1977 made the key discovery. Just as a black-hole horizon has a temperature and an entropy, the cosmological event horizon of de Sitter space does too. Every observer is surrounded by a horizon that emits a faint thermal glow, the Gibbons-Hawking radiation, at a temperature set by the expansion rate. For our measured dark energy this temperature is around 10^-30 kelvin, fantastically cold but not exactly zero.
This reframes the ending. Rather than a simple run-down to absolute zero, the universe reaches a stationary thermal state in equilibrium with its own horizon. Andreas Albrecht and collaborators, from 2004 onward, pushed this into a research program, de Sitter equilibrium cosmology, that treats this horizon-dominated thermal state as the fundamental long-term condition and asks what physics, including the rare thermal fluctuations it permits, looks like from inside it.
The family stance
The universe ends by expanding forever and running down. There is no recollapse and no tearing apart, just an ever-thinner, ever-colder space approaching thermodynamic equilibrium. This is the fate implied by the standard cosmological model if dark energy is a cosmological constant or close to one.
§2.5 · Evidence
- The Gibbons-Hawking result is a direct, widely accepted consequence of quantum field theory in curved spacetime, the same framework that gives black holes a temperature
- Current data showing w consistent with -1 imply that an asymptotic de Sitter state is the natural geometric endpoint of the standard cosmology
- Horizon thermodynamics has become a standard tool, linking this end state to holographic and entropic-gravity ideas elsewhere in the catalog
§3 · What you'd need to test it
- An eternally accelerating universe asymptotes to de Sitter geometry, fixed by the value of the cosmological constant
- The cosmological event horizon carries a Gibbons-Hawking temperature near 10^-30 kelvin for the observed dark-energy density
- The horizon has a finite entropy set by its area, which caps the information accessible to any single observer
- Rare thermal fluctuations of the horizon are possible in principle, which is the basis of the Boltzmann-fluctuation concern discussed below
§4 · Where it breaks
- The de Sitter equilibrium program is far less settled than the Gibbons-Hawking result it builds on; treating the horizon-thermal state as fundamental is a frontier interpretive move, not consensus
- Eternal de Sitter space permits rare thermal fluctuations that, given infinite time, could produce freak observers (Boltzmann brains) far more often than ordinary ones; many take this as a reductio that disfavours a truly eternal de Sitter future rather than a real prediction
- Whether the de Sitter vacuum is even stable over the longest timescales is contested, with swampland-type arguments suggesting it may not be, which would undercut the whole picture
Go deeper
Gibbons and Hawking 1977 (Phys. Rev. D 15, 2738) generalised black-hole thermodynamics to cosmological horizons. The temperature is T equal to H over 2π in natural units, where H is the de Sitter Hubble rate, and the horizon entropy is one quarter of its area in Planck units. For the observed dark-energy density this gives a temperature around 10^-30 kelvin and an enormous but finite horizon entropy. This is a pre-arXiv paper, cited here without an arXiv identifier per the catalog convention.
The Boltzmann-brain problem is the sharpest objection. In an eternal de Sitter space, thermal fluctuations of the horizon can in principle assemble any configuration, including a self-aware observer, at some tiny but nonzero rate. Over infinite time such freak observers would vastly outnumber ordinary ones, making our ordered observations statistically absurd. Many cosmologists regard Boltzmann-brain domination as a serious consistency problem for a literally eternal de Sitter future, which is why this catalog folds Boltzmann brains in here as a consistency check rather than listing them as a standalone fate.
Cross-references: the horizon thermodynamics here connects directly to the Chapter 3 Emergent Spacetime family, where entropic and holographic arguments treat horizon entropy as fundamental, and to Hawking radiation in Chapter 6, which is the black-hole analogue of the same effect. The de Sitter stability question links to the Swampland Program variant in the Chapter 4 String Theory family.
Variants in this family
Compare variants▸§5 · Who built it, and when(3 sources, 3 established)
- EstablishedGibbons, G. W. & Hawking, S. W. (1977). 'Cosmological event horizons, thermodynamics, and particle creation.' Phys. Rev. D 15, 2738
- EstablishedDyson, L., Kleban, M. & Susskind, L. (2002). 'Disturbing Implications of a Cosmological Constant.' JHEP 0210, 011
- EstablishedAlbrecht, A. & Sorbo, L. (2004). 'Can the universe afford inflation?' Phys. Rev. D 70, 063528
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