Cited by 340Cosmology and Gravitation TheoriesBlack Holes and Theoretical PhysicsNoncommutative and Quantum Gravity Theories

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Disturbing Implications of a Cosmological Constant

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Dyson, Lisa, Kleban, Matthew, Susskind, Leonard·2002·Journal of High Energy Physics

DOI 10.1088/1126-6708/2002/10/011

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Crossref · 10.1088/1126-6708/2002/10/011

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Claims the paper makes

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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This solution makes manifest that the energy is independent of the matter content of the space.”
- Also stated in: § JHEP10(2002)011 · plain
  “Since ∂ ρ Z = 1, the energy is independent of the matter content of the space.”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
Load-bearingStrength:boosted· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
In the paper
“This bound can easily be shown to be equivalent to the covariant entropy bound as proposed in [31].”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
What the sources say
- Not checked yetcites [31] S.W. Hawking, 1996, Class. Quantum Grav. source
Strength:plain· not yet calibratedCausal:correlational· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The implication of such a description, as we have suggested in section 1, is that Poincaré recurrences are inevitable.”
- Also stated in: § 5. Complementarity and its implications · boosted
  “Given our assumptions, the conclusion that such Poincaré recurrences of the universe occur is unavoidable.”
§ Disturbing implications of a cosmological constant > 5. Complementarity and its implications
Load-bearingStrength:boosted· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- The authors state this as an assumption: The physics inside an observer's causal patch is exactly described by a dual quantum system with a Hamiltonian and a space of states, and the state is a thermal density matrix exp(−βH) at the appropriate temperature.
- The authors state this as an assumption: The maximum entropy the system can ever have is the entropy of a de Sitter space whose size is set by the cosmological constant.
- The authors state this as an assumption: Horizon Complementarity is taken to mean that physics in the causal patch can be described as a closed or isolated system using conventional quantum mechanics.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As we shall see, it implies that the universe has neither JHEP10(2002)011 a beginning nor and end.Instead, it intermittently recycles itself, but in a way that is very different from so called cyclic universes.”
§ Disturbing implications of a cosmological constant > 5. Complementarity and its implications
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- The authors state this as an assumption: The physics inside an observer's causal patch is exactly described by a dual quantum system with a Hamiltonian and a space of states, and the state is a thermal density matrix exp(−βH) at the appropriate temperature.
- The authors state this as an assumption: Horizon Complementarity is taken to mean that physics in the causal patch can be described as a closed or isolated system using conventional quantum mechanics.

Show all 40 claims

It may state two separate claims as one. 39
The quote only partly states this claim. 13
Probably not a substantial claim. 10

A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The reason is that the causal patch does not have the analog of an ultraviolet boundary.Because AdS has such a boundary it is possible to modify the boundary conditions without changing the fact that the bulk theory still satisfies the bulk field equations.Without such a boundary there is no way to do the same for de Sitter space.”
§ Disturbing implications of a cosmological constant > 5. Complementarity and its implications
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
- The authors state this as an assumption: The ideas of holography and complementarity can be applied to de Sitter space.
In the paper
“On the average it is in a steady state of thermal equilibrium.”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
What the sources say
- Not checked yetcites [23] source
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
Probably not a substantial claim.
- The authors state this as an assumption: The usual connections between quantum statistical mechanics and thermodynamics hold.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This implies an initial holographic entropy of about 10 10 , which is extremely small by comparison with today's visible entropy.”
§ Disturbing implications of a cosmological constant > 1. Recurrent cosmology
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
- The authors state this as an assumption: The universe began with an inflationary phase and will end in an accelerated de Sitter phase.
In the paper
“In other words, the theory describes a closed isolated box bounded by the observer's horizon, and makes reference to no other region.”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
What the sources say
- Not checked yetcites [2] source
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
- The authors state this as an assumption: The holographic and horizon complementarity principles are valid assumptions for describing horizons.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From the fact that the entropy is finite, it follows that the energy levels are discrete and that the number of levels below any given energy is finite.”
§ Disturbing implications of a cosmological constant > 5. Complementarity and its implications
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
- The authors state this as an assumption: The physics inside an observer's causal patch is exactly described by a dual quantum system with a Hamiltonian and a space of states, and the state is a thermal density matrix exp(−βH) at the appropriate temperature.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The conventional view is that the universe will end in a de Sitter phase with all matter being infinitely diluted by exponential expansion.”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✗ Asserted: fails✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
Probably not a substantial claim. The authors may not put it forward as true. It may state two separate claims as one.
- The authors state this as an assumption: The universe began with an inflationary phase and will end in an accelerated de Sitter phase.
None of the sources cited for this claim have been checked yet.
In the paper
“Then on time scales of order T r ∼ exp S (1.1) the system will undergo Poincaré recurrencesfoot_2 [8,9].”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
What the sources say
- Not checked yetcites [8] W. Fischler
- Not checked yetcites [9] L. Dyson, 2002, J. High Energy Phys. source
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“These assumptions-together with the existence of a final cosmological constant-imply that the universe is eternal but finite.”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
- The authors state this as an assumption: The universe began with an inflationary phase and will end in an accelerated de Sitter phase.
- The authors state this as an assumption: A final cosmological constant exists.
- The authors state this as an assumption: The usual connections between quantum statistical mechanics and thermodynamics hold.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Starting in a high entropy,”
§ Disturbing implications of a cosmological constant > 5. Complementarity and its implications
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
The quote only partly states this claim.
- The authors state this as an assumption: The physics inside an observer's causal patch is exactly described by a dual quantum system with a Hamiltonian and a space of states, and the state is a thermal density matrix exp(−βH) at the appropriate temperature.
- The authors state this as an assumption: The maximum entropy the system can ever have is the entropy of a de Sitter space whose size is set by the cosmological constant.
None of the sources cited for this claim have been checked yet.
In the paper
“The remedy suggested by the black hole analogue is obvious; restrict all attention to a single causal patch [5,8,9].”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
What the sources say
- Not checked yetcites [5] source
- Not checked yetcites [8] W. Fischler
- Not checked yetcites [9] L. Dyson, 2002, J. High Energy Phys. source
Load-bearingStrength:hedged· not yet calibrated
Tests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✓ Based: passes
Probably not a substantial claim. It may be too vague to check against evidence.
None of the sources cited for this claim have been checked yet.
In the paper
“We now know that this is an artifact of trying to describe the complex interacting degrees of freedom of the horizon by quantum field theory defined on both the interior and exterior of the black hole.”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
What the sources say
- Not checked yetcites [1] L. Susskind
- Not checked yetcites [2] source
Load-bearingStrength:boosted· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
- The authors state this as an assumption: The holographic and horizon complementarity principles are valid assumptions for describing horizons.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This implies that the horizon entropy within the causal patch in the far future and past is bounded in the ordinary way.”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one. The quote only partly states this claim.
- The authors state this as an assumption: The universe began with an inflationary phase and will end in an accelerated de Sitter phase.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Horizon Complementarity then says the universe is described by any observer as a closed and finite system.”
§ Disturbing implications of a cosmological constant > 5. Complementarity and its implications
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
Probably not a substantial claim.
- The authors state this as an assumption: Horizon Complementarity is taken to mean that physics in the causal patch can be described as a closed or isolated system using conventional quantum mechanics.
In the paper
“This system, although unrealistic as a cosmology, is extremely well understood through the AdS/CFT duality.”
§ Disturbing implications of a cosmological constant > 2. The AdS black hole as a cosmology
What the sources say
- Not checked yetcites [19] S. Hawking, 1983, Comm. Math. Phys. source
Load-bearingStrength:boosted· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For a perturbation on the past boundary to influence the causal patch, the signal must pass through the past horizon of the observer.However the past horizon is just the infinite past t = -∞.”
- Also stated in: § JHEP10(2002)011 · boosted
  “Obviously, any such perturbation of a finite entropy thermal cavity will re-thermalize after a finite time.In fact, at any finite time, an infinite number of Poincaré recurrences have already occurred.”
§ Disturbing implications of a cosmological constant > JHEP10(2002)011
Load-bearingStrength:boosted· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
- The authors state this as an assumption: The physics inside an observer's causal patch is exactly described by a dual quantum system with a Hamiltonian and a space of states, and the state is a thermal density matrix exp(−βH) at the appropriate temperature.
- The authors state this as an assumption: The maximum entropy the system can ever have is the entropy of a de Sitter space whose size is set by the cosmological constant.
In the paper
“The quantum Poincaré Recurrence theorem is similar and can be stated as follows: given a system in which all energy eigenvalues are discrete, a state will return arbitrarily close to its initial value in a finite amount of time.”
§ Disturbing implications of a cosmological constant > Additional information
What the sources say
- Not checked yetcites [25]-[27]
Strength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passes
Probably not a substantial claim. The paper’s conclusions may not depend on it.

48 of 48

The authors state this as an assumption.
The universe began with an inflationary phase and will end in an accelerated de Sitter phase.
“Present cosmological evidence points to an inflationary beginning and an accelerated de Sitter end.”
The authors state this as an assumption.
A final cosmological constant exists.
“These assumptions-together with the existence of a final cosmological constant-imply that the universe is eternal but finite.”
The authors state this as an assumption.
The usual connections between quantum statistical mechanics and thermodynamics hold.
“In the following we will assume the usual connections between quantum statistical mechanics and thermodynamics.”
The paper relies on this without support.
There is no universally accepted explanation for how the universe reached its exceptionally low-entropy initial state.
“However, there is no universally accepted explanation of how the universe got into such a special state.”
The paper relies on this without support.
Neither string theory nor quantum gravity currently provides a consistent account of the initial singularity or the low initial entropy.
“Neither string theory nor quantum gravity provide a consistent starting point for a discussion of the initial singularity or why the entropy of the initial state is so low.”
The paper relies on this without support.
The late-time behavior of a universe with a cosmological constant is not well understood.
“The late time features of a universe with a cosmological constant are also not well understood.”
The authors state this as an assumption.
The holographic and horizon complementarity principles are valid assumptions for describing horizons.
“under a set of assumptions motivated by the holographic and horizon complementarity principles”
The authors state this as an assumption.
The physics inside an observer's causal patch is exactly described by a dual quantum system with a Hamiltonian and a space of states, and the state is a thermal density matrix exp(−βH) at the appropriate temperature.
“We assume that the physics within the causal patch is exactly described by a dual quantum system that includes a hamiltonian H and a space of quantum states.Furthermore the state of the world within the causal patch is density matrix exp (-βH) with the appropriate temperature.”
The authors state this as an assumption.
The maximum entropy the system can ever have is the entropy of a de Sitter space whose size is set by the cosmological constant.
“Furthermore we assume that the maximum entropy that the system can ever have is given by the entropy of a de Sitter space, whose size is determined by the cosmological constant.”
The authors state this as an assumption.
There is a fundamental cosmological constant.
“• There is a fundamental cosmological constant.”
The authors state this as an assumption.
The ideas of holography and complementarity can be applied to de Sitter space.
“• We can apply the ideas of holography and complementarity to de Sitter space.”
The authors state this as an assumption.
The time evolution operator is unitary, so phase-space area is conserved.
“• The time evolution operator is unitary, so that phase space area is conserved.”
The authors state this as an assumption.
The observer's proper time goes to infinity in the remote past and remote future, and the trajectory does not hit a singularity in finite proper time.
“We have made the assumption that the proper time along the observer's trajectory goes to infinity in the remote past and the remote future; i.e., the trajectory does not encounter a singularity in finite proper time.”
The authors state this as an assumption.
Horizon Complementarity is taken to mean that physics in the causal patch can be described as a closed or isolated system using conventional quantum mechanics.
“For our present purposes, Horizon Complementarity will be taken to mean that physics in the causal patch can be described in terms of a closed or isolated system described by conventional quantum mechanics.”

14 of 14

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

Covariant entropy bound points to the wrong reference
Minor
The cited entry [31] concerns the gravitational Hamiltonian. The reference list instead identifies [32] as the covariant entropy conjecture.
Both ring metrics are assigned to the inside region
Minor
The first metric is described as the solution outside the ring, but its stated range is r < r0. The metric explicitly described as inside the ring has the same range, leaving no stated range for the exterior solution.
Entropy formula has the opposite sign
Minor
For a normalized density matrix, Trρ log ρ is nonpositive. It therefore cannot equal the stated entropy, which is the logarithm of a number of effective states.

3 of 3

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Authors: Dyson, L., Kleban, M., & Susskind, L.
Affiliations: Massachusetts Institute of Technology (US)
Stanford University (US)
ORCID: Kleban, Matthew
Susskind, Leonard
Venue: Journal of High Energy Physics
Publisher: Springer Science and Business Media LLC
Published: 2002-10-02
Volume: 2002
Issue: 10
Pages: 011-011
ISSN: 1029-8479 (ISSN-L)
DOI: 10.1088/1126-6708/2002/10/011
OpenAlex: W2141674504
Cited by: 338
References: 22
Citations by year: 2026: 6 · 2025: 11 · 2024: 15 · 2023: 20 · 2022: 20 · 2021: 18 · 2020: 9 · 2019: 28 · 2018: 7 · 2017: 14 · 2016: 12 · 2015: 7 · 2014: 8 · 2013: 8 · 2012: 14
FWCI: 11.63
Type: journal article
Language: en
Open access: bronze
doi.org
Locations: Journal of High Energy Physics (publishedVersion)
arXiv (Cornell University) (submittedVersion)
arXiv (Cornell University)
Funders: National Science Foundation (9870115)
Mellam Family Foundation
Topics: Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
Keywords: cosmological constant, holographic principle, causal patch, cosmological evolution, spacetime structure, cosmological paradoxes, quantum gravity

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