Quantum Cosmology Without Singularities: A New Approach

Artyom V. Yurov; Valerian A. Yurov

REVIEW 4 major objections 5 minor 58 references

Quantum Cosmology Without Singularities: A New Approach

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper claims that placing a zero-scale-factor universe at the bottom of a many-interacting-universes ensemble makes the quantum interaction diverge as the neighboring universe shrinks, forcing a bounce and eliminating the Big Bang…

desk verdict A concrete, honestly delimited idea about adding Barrow's zero universe to the MIU ensemble, with useful exactly solved examples, but the two headline theorems are not proven as written. read the letter →

arxiv 2505.02616 v3 pith:LJEGWTF6 submitted 2025-05-05 gr-qc hep-th

Valerian A. Yurov , Artyom V. Yurov This is my paper · ORCID

classification gr-qchep-th PACS 04.60.-m98.80.Qc

keywords quantumcosmologymanyinteractinguniverseszerouniversecosmologicalsingularityBigRippotentialscalefactorbouncing

topics Quantum Gravity

open problems Quantum Gravity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Quantum cosmology usually inherits classical singularities unless extra physics is added. This paper argues that within the many-interacting-universes (MIU) quantization scheme, the mere presence of a "zero universe"—an exact solution of the field equations of general relativity whose scale factor is identically zero—removes the Big Bang, Big Crunch, and Big Rip. The mechanism is a quantum potential between universes ordered by scale factor: with the zero universe at the bottom, the potential contains a term $\sim a_2^{-2}$ for the next universe, and because that second universe is assumed empty, nothing can cancel the repulsion as $a_2\to0$, so the collapse stops and bounces. The same mechanism, via a linear-independence argument, also prevents phantom-filled universes from running away to infinite scale factor. If correct, it means classical cosmological singularities are artifacts of neglecting zero universes in quantization, rather than unavoidable features of gravity.

What carries the argument

The central object is the quantum interaction potential $U(a_1,\dots,a_N)=\sum_{n=1}^N (1/(a_{n+1}-a_n)-1/(a_n-a_{n-1}))^2$ with boundary conditions $a_0=a_{N+1}=\infty$, the same potential that defines the many-interacting-worlds quantization. Its role here is to make the Hamiltonian constraint (17) divergent at small $a_2$ once $a_1\equiv0$, because the first term becomes $1/a_2^2$; Condition 3 (an empty second universe) guarantees no density or pressure term can cancel that divergence, so $a_2$ bounces at a minimum radius. The second piece of machinery is a linear-independence trick: from a solution $a_n$ one constructs a partner $\hat a_n=a_n\int dt/a_n^2$ with unit Wronskian, and a finite-time Big Rip in $a_n$ forces the partner to vanish, contradicting the no-zero-scale-factor theorem.

What would settle it

Relax Condition 3 by giving the second universe a small radiation density $\rho_2=R^2/a_2^4$ and integrate the two-universe equation (33); the paper's own exact solutions (42)–(43) then start from $a_2(0)=0$, which is a singularity. A numerical scan in $R^2$ would map the critical density at which the bounce is lost, settling whether emptiness is essential.

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Extended reading notes

Core claim

The paper's central claim is that under three conditions—ordered scale factors, the smallest universe being the identically zero scale-factor solution ($a=\dot a=0$), and the second universe being completely empty—every solution of the MIU equations (16)–(17) has $a_n(t)>0$ for all $n>1$ and all times, and no solution reaches a Big Rip at $a_n=\infty$. The load-bearing fact is that the quantum potential $U(a_1,\dots,a_N)=\sum_n (1/(a_{n+1}-a_n)-1/(a_n-a_{n-1}))^2$, with $a_1\equiv0$, contains a term $1/a_2^2$, so in the constraint (17) it diverges as $a_2\to0$; with $\rho_2=p_2=0$ there is no matter term to compensate, forcing $a_2$ to obey a first integral whose minimum radius is set by the quantum-gravity length scale. The proof then propagates positivity upward: if any $a_n$ were to vanish, the ordering forces lower neighbors to vanish simultaneously, and the same constraint is violated. The Big Rip theorem follows from considering a linearly independent partner solution built by a Wronskian formula; if the largest universe reached infinite scale factor in finite time, that partner would have to vanish there, contradicting the positivity theorem. Thus singularities are claimed to be kinematically excluded by the interaction structure rather than by any special matter content.

Load-bearing premise

The whole no-singularity result depends on the second universe (the one right above the zero universe in the scale-factor ordering) being completely empty: the paper's own two-universe solutions show that filling it with radiation ($w=1/3$) brings the singularity back.

Editorial extensions

If this is right

In any ensemble satisfying the three conditions, every universe with $n>1$ keeps a strictly positive scale factor; gravitational collapse ends in a bounce rather than a crunch.
Universes containing phantom fields with $w<-1$ never reach a Big Rip: the positivity theorem for the partner solution forbids the infinite-scale-factor endpoint.
The zero universe is an exact solution of the field equations (a special case of the closed stationary quintessence solution), so any quantization that sums over all geometries must include it.
In the classical limit $\hbar\to0$ the MIU equations reduce to the standard non-interacting cosmological equations, recovering ordinary decoherence and the classical Friedmann dynamics.
Quantum effects in this scheme act on cosmological horizon scales, so they modify the expansion dynamics rather than only seeding small fluctuations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The emptiness of the second universe looks like an ad hoc condition; a natural extension would be to find the largest density or the equation-of-state threshold in that universe for which the $1/a_2^2$ repulsion still wins, using the paper's integrable two-universe equation.
The Wronskian argument is a general mechanism: it suggests that any finite-time singularity that makes two solutions of the same second-order equation coalesce would be forbidden, so the method might extend to Sudden or Big Freeze singularities that the paper explicitly leaves out.
If zero universes are truly mandatory, the same idea should appear in functional-integral quantization as a boundary contribution at $a=0$; one could test whether adding it changes the tunneling wave function of the universe.
The minimum radius predicted by solutions like Eq. (35) is a concrete, testable signature: bounce models predict a stochastic gravitational-wave background, and limits on it constrain the minimum scale factor.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things up front. First, the paper's core idea is genuinely new: putting Barrow's a=0 solution into the Hall–Deckert–Wiseman multiverse ensemble and letting the 1/a_2^2 term in the quantum potential act as a barrier. The exactly solved two- and three-universe examples in Sec. 5 are the best part of the paper and they do support the mechanism in integrable cases. Second, the two theorems that carry the advertised conclusions are not proven. Theorem 1's proof simply omits Case (ii), the 'master-factor' limit after Eq. (29), saying the calculation is straightforward. That is a gap, but not fatal by itself. Theorem 2 has a load-bearing mathematical error: Eq. (65) defines \hat a_n so that the Wronskian W(a_n,\hat a_n)=1 identically, but Step 5 claims the Wronskian tends to 0 as t\to t_s. The limit (67) only shows d/dt(\hat a_N/a_N)\to 0; the compensating divergence in a_N^2 is dropped. So the contradiction that is supposed to eliminate the Big Rip does not follow. The stress-test note is right about this, and it is the decisive unsupported step in the paper's headline claim.

What the paper does well: it is honestly delimited. The preface explicitly lists what the method does not cover, the limitations section is unusually forthcoming, and the authors do not pretend to have observational predictions. The radiation-filled second-universe example in Sec. 5.1 is good, honest work, and it also reveals the fragility of the mechanism: when the second universe is radiation rather than empty, the exact solution is singular at t=0. In other words, Condition 3 -- that the second universe is completely empty -- is not a physically motivated selection but an ad hoc postulate that is doing almost all of the work. The paper's own examples show the conclusion does not survive without it.

I disagree with the reader's lowest circularity score, by the way. The model is explicit and self-contained; the conditions are chosen to make the theorem work, but the equations are not fitted to data and the borrowed pieces are re-derived in the appendix. The citation pattern is basically fine, with relevant self-citations.

Who is this for? Someone working in pilot-wave cosmology or in singularity avoidance in quantum cosmology might want to read Secs. 2 and 5 and may find the exact solutions useful. The abstract's claim that Big Bang, Big Crunch and Big Rip 'all fail to arise' is not supported by the supplied proof. I would not cite it as a proof of singularity avoidance, and I would not bring it to reading group as a confirmed result.

Would I send this to a referee? Yes. The claims are checkable, the mechanism is concrete, and the mathematical flaws deserve formal adjudication rather than a desk reject. My expectation is that a careful referee will ask for a corrected Theorem 2 or a withdrawal of the Big Rip claim, and a completed proof of Theorem 1's missing case. As it stands, the paper is a promising model-building exercise with an unproven headline.

Referee Report

4 major / 5 minor

Summary. The paper proposes a quantization of FLRW cosmology using Hall-Deckert-Wiseman's many-interacting-worlds idea, applied to an ensemble of universes (MIU). The key new ingredient is the inclusion of a Barrow 'zero universe' (a_1(t)=0 identically) plus an empty second universe. The authors claim two theorems: Theorem 1 (Sec. 4) states that under Conditions 1–4 the scale factors a_n for n>1 are strictly positive, eliminating Big Bang and Big Crunch singularities; Theorem 2 (Sec. 6.2) claims that under Conditions 1–3 no Big Rip singularities occur. The paper also presents exact solutions for N=2 and N=3 interacting universes, discusses the classical limit, and speculatively connects the framework to decoherence in eternal inflation and the low-entropy initial state problem.

Significance. If the two theorems were correct, the result would be remarkable: a purely kinematic quantum potential, arising from the mere presence of a zero-scale-factor universe, would eliminate all three standard cosmological singularity types. The paper contains concrete, checkable exact solutions in Sec. 5, and it is honest in listing its limitations. Those strengths, however, are undermined by serious gaps in the general proofs: Theorem 1's proof omits an entire case, and Theorem 2's proof rests on an invalid Wronksian limit. The central claims are therefore not established, and the advertised singularity-avoidance mechanism is not proven beyond the special solved examples.

major comments (4)

[§4, after Eq. (29)] The proof of Theorem 1 explicitly omits the entire Case (ii), the 'master-factor' limit in which a_k/a_{k+1} tends to a constant as t→0. The text states 'We will omit the calculations since they are again rather straightforward...'. This is one of two exhaustive cases into which the dichotomy is split; without a proof for Case (ii), Theorem 1 is not fully proven. The omitted calculation must be supplied, or the proof restructured.
[§6.2, Step 5, Eqs. (65)–(68)] The Wronksian argument in Theorem 2 is invalid. Equation (65) defines \hat{a}_n so that W(a_n,\hat{a}_n)=a_n^2 d/dt(\hat{a}_n/a_n)=1 identically. Therefore the limit in (68), \lim_{t→t_s} W(a_N,\hat{a}_N)→0, is false; the Wronksian remains 1. The inference from (67) that \hat{a}_N→C a_N is also not justified: a vanishing derivative of the ratio does not imply a vanishing Wronksian. The claimed contradiction with linear independence is therefore manufactured, and the proof of Theorem 2 collapses at this step.
[§6.2, Step 5] Even if the Wronksian issue were repaired, the application of Theorem 1 to the 'dressed' scale factors \hat{a}_n is not justified. The construction in Steps 3–4 generally destroys Condition 1: the paper itself notes that the ordering is usually inverted (\hat{a}_n > \hat{a}_{n+1} for n>2). No verification is given that the new densities \hat{\rho}_n, \hat{p}_n satisfy Condition 4. Thus the contradiction with Theorem 1 is doubly unsupported.
[§3, Condition 3, and §5.1] The entire no-singularity mechanism depends on the ad hoc postulate that the second universe is completely empty (ρ_2=p_2=0). Section 5.1 shows this is load-bearing: when the second universe is filled with radiation (w=1/3), the exact solutions (42) and (43) are singular at t=0 despite the presence of the zero universe. The paper offers no physical justification for why the universe immediately above the zero universe must be empty, which sharply limits the generality of the claimed singularity avoidance. This is a significance issue, but it is essential to the advertised conclusion.

minor comments (5)

[Throughout] The manuscript contains many typographical errors and stylistic infelicities ('Ineracting', 'monographes', 'scoop', 'peturbativity', 'googleplex'), which should be corrected in any revision.
[Preface] The Preface's direct address to the reader and its comments about LLM summaries are out of place in a formal journal article; the authors should condense it to a standard abstract and introduction.
[§3, Condition 4] Condition 4 is imprecise: 'ρ_n has but one special point that occurs only when a_n→0' should be defined mathematically (e.g., ρ_n is C^1 on (0,∞) and bounded away from a_n=0). As written, it is too vague to be used in a proof.
[References] Reference [24] is listed as 'A private correspondence with Artyom V. Astashenok'; this is not a citable reference and should be replaced by a published source or removed.
[§5.1] In the paragraph after Eq. (36), the text says the period 'does not depend on L^2_{PL}' but the expressions for x_max and x_min do depend on L_PL; the statement is correct but could be clarified to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the theorems are conditional consequences of the explicitly stated MIU equations and assumptions, with self-citations non-load-bearing.

full rationale

The paper's central results are conditional mathematical consequences of its explicitly stated model, not circular reductions. Equations (16)-(17) and the quantum potential (14) define the MIU dynamics; the model is an assumption, and the theorems state implications of that assumption. Theorem 1 (Sec. 4) concludes a_n>0 for n>1 under Conditions 1-4; Condition 3 (Eq. (20)) does not assert positivity of a_2, so the conclusion is not contained in the assumptions. The proof uses the divergence of U in (25) and the constraint (17), plus the explicit solution (32), which is a real derivation. The exact solutions of Sec. 5 are solved from the stated equations, not fitted to the theorem. The authors' self-citations ([1], [2], [47], [48]) support the MIW/MIU formalism and a standard reduction-of-order technique, but Appendix A re-derives the potential, and the cited results are not unverified uniqueness claims; they are not load-bearing in the circularity sense. I flag, as non-circular caveats: Condition 3 is a strong ad hoc emptiness postulate that the paper itself shows is necessary (Sec. 5.1, radiation case, Eqs. (42)-(43)); Theorem 1 Case (ii) omits the promised calculations; and Theorem 2 Step 5 contains a likely invalid limit (Eq. (68) ignores that W≡1 by (65)) and invokes Theorem 1 although Condition 4 is dropped. These are rigor/correctness defects, not examples of a fitted input relabeled as a prediction or a conclusion defined into existence. Therefore no load-bearing circular step is exhibited; score 0.

Assumptions & free parameters 0 free parameters · 6 assumptions · 3 invented entities

The paper postulates the MIU dynamics (16)-(17) with the quantum potential (14), then adds three structural assumptions: the physical legitimacy of the zero-universe solution, the emptiness of the second universe (Condition 3), and a vaguely stated energy-condition condition (Condition 4). No numerical parameters are fitted to data; the integration constants in the exact solutions are not free parameters. The theorem's dependence on Condition 3 is explicit and is demonstrated by the paper's own radiation counterexample, so the ledger flags it as ad hoc.

assumptions (6)

domain assumption The Many Interacting Universes dynamics (16)-(17) with quantum potential (14) is a valid quantization of cosmological gravity.
The paper operates entirely within this pilot-wave framework imported from Hall-Deckert-Wiseman [1] and the authors' earlier MIU paper [2].
domain assumption The Barrow zero universe a(t) = 0 (with formally infinite density) is a physically permissible solution of Einstein equations that must be included in the ensemble.
Section 2 derives a = 0 as the alpha to 8 pi G / (3 c^2) limit of Einstein quintessence; the limit has zero scale factor and divergent density, so its physical admissibility is assumed.
ad hoc to paper Condition 3: the second universe contains no matter (rho_2 = p_2 = 0).
Load-bearing for Theorem 1; Sec. 5.1 shows singular solutions reappear if the second universe is filled with radiation.
ad hoc to paper Condition 4: standard energy conditions hold and densities have a single singular point only as a_n approaches 0.
Needed to prevent matter divergences from canceling the quantum potential divergence in (17); the formulation is vague.
domain assumption Existence of global smooth solutions of (16)-(17) on the relevant interval.
The theorems assume solutions exist up to the would-be singularity; no global existence proof is given.
ad hoc to paper The dressing construction of Theorem 2 yields a genuine new solution (hat a_n, hat rho_n, hat p_n) of (16)-(17).
Step 4 of Sec. 6.2 sketches the construction and derives new densities via continuity; global validity is not established.

invented entities (3)

Barrow zero universe
purpose: Fixed member of the ensemble with a_1 = 0, generating the 1/a_2^2 barrier in U
No observational handle; it is a degenerate limit solution of Einstein equations with infinite density.
Empty buffer universe
purpose: Second universe with rho_2 = p_2 = 0, whose repulsion by the zero universe produces a nonsingular bounce (32)
Ad hoc condition 3; the paper shows the theorem fails if this universe is filled with radiation.
Dressed universes
purpose: Conjugate scale factors hat a_n used in the Big Rip contradiction proof
Pure proof devices; no physical reality claimed.

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Cite this review

Pith. "Pith review of Quantum Cosmology Without Singularities: A New Approach." pith.science (2026). https://pith.science/paper/LJEGWTF6

@misc{pith2026250502616,
  author       = {Pith},
  title        = {Pith review of: Quantum Cosmology Without Singularities: A New Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LJEGWTF6}},
  note         = {Machine review of arXiv:2505.02616}
}

read the original abstract

The article is dedicated to a discussion regarding the role of Barrow's ''Zero Universes'' in quantum cosmology. In particular, we demonstrate that if quantum gravity effects are modeled by the quantum potential method associated with the ''many interacting universes'' (MIU) model, then the mere presence of the universes with a zero scale factor (the ``Zero universes'') produces a veritably remarkable outcome: the classical cosmological singularities of Big Bang, Big Crunch and Big Rip all fail to arise. In other words, those universes that are considered ill-posed at the classical level may turn out to be a necessary and sought-after ingredient in a future internally consistent quantum theory of gravity. Finally, we argue that the MIU quantization method might shed light on a number of other cosmological mysteries; for example, it might account for a decoherence which preceded the eternal inflation, and elucidate how the quantum superposition of vacuum decays occurring at different places might give birth to actual bubble universes there. In addition, the new method might help explain why our universe was born in an extremely low-entropy initial state required to trigger the initial inflation.

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Reference graph

Works this paper leans on

58 extracted references · 55 canonical work pages

[1]

M. J. W. Hall, D.-A. Deckert and H. M. Wiseman, ”Quantum phenom- ena modelled by interactions between many classical worlds”,Phys. Rev. X4(2014) 041013

work page 2014
[2]

A. V. Yurov, V. A. Yurov, ”The day the universes interacted: quantum cosmology without a wave function”,Eur. Phys. J. C79(2019) 771

work page 2019
[3]

Perturbations and Linearization Stability of Closed Friedmann Universes

John D. Barrow, ”Is the universe ill-posed?”, http://arxiv.org/abs/2003.14108v2

work page Pith review arXiv 2003
[4]

Raphael Bousso and Leonard Susskind, ”Multiverse interpretation of quantum mechanics”,Phys. Rev. D85(2012) 045007

work page 2012
[5]

Roger Penrose, ”Cycles of Time: An Extraordinary New View of the Universe”, Random House (USA) (2010)

work page 2010
[6]

Sean Carroll, ”From Eternity to Here: The Quest for the Ultimate The- ory of Time”, Hardcover – January 7, (2010)

work page 2010
[7]

Bouhmadi-Lopez, P

M. Bouhmadi-Lopez, P. F. Gonz´ alez-D´ ıaz and P. Martin- Moruno,”Worse than a big rip?”,Phys. Lett. B659(2008) 1–5

work page 2008
[8]

A. V. Yurov, A. V. Astashenok and P.F. Gonz´ alez-D´ ıaz, ”Astronomical bounds on future big freeze singularity”,Grav. Cosmol.14No. 3 (2008) 205–212

work page 2008

Show all 58 references

[9]

Cannata, A

F. Cannata, A. Yu. Kamenshchik and D. Regoli, ”Scalar field cosmo- logical models with finite scale factor singularities”,Phys. Lett. B670 (2009) 241–245

2009
[10]

Shtanov and V

Y. Shtanov and V. Sahni, ”New Cosmological Singularities in Braneworld Models”,Class. Quant. Grav.19(2002) L101–L107. 53

2002
[11]

J. D. Barrow, ”Sudden Future Singularities”,Class. Quant. Grav.21 (2004) L79–L82

2004
[12]

J. D. Barrow, ”More General Sudden Singularities”,Class. Quant. Grav. 21(2004) 5619–5622

2004
[13]

J. D. Barrow,”New Isotropic and Anisotropic Sudden Singularities”, Class. Quant. Grav.22(2005) 1563–1571

2005
[14]

J. D. Barrow, ”New Anisotropic Sudden Singularities and Dimensional Reduction”,Phys. Rev. D102(2020) 024073

2020
[15]

Barrow, Spiros Cotsakis and Dimitrios Trachilis, ”The Generic Sudden Singularity in Brans-Dicke Theory”,Eur

John D. Barrow, Spiros Cotsakis and Dimitrios Trachilis, ”The Generic Sudden Singularity in Brans-Dicke Theory”,Eur. Phys. J. C80(2020) 1197

2020
[16]

Barvinsky, C

A.O. Barvinsky, C. Deffayet and A. Y. Kamenshchik, ”Anomaly Driven Cosmology: Big Boost Scenario and AdS/CFT Correspondence”,JCAP 0805 (2008) 020

2008
[17]

Gorini, A

V. Gorini, A. Kamenshchik, U. Moschella and V. Pasquier,”Tachyons, Scalar Fields and Cosmology”,Phys. Rev. D69(2004) 123512

2004
[18]

Keresztes, L

Z. Keresztes, L. A. Gergely, V. Gorini, U. Moschella and A. Yu. Ka- menshchik, ”Tachyon cosmology, supernovae data and the Big Brake singularity”,Phys. Rev. D79(2009) 083504

2009
[19]

Nojiri, S.D

S. Nojiri, S.D. Odintsov and S. Tsujikawa, ”Properties of singularities in (phantom) dark energy universe”,Phys. Rev. D71(2005) 063004

2005
[20]

A. V. Yurov, ”Brane-like singularities with no brane”,Phys. Lett. B689 (2010) 1–7

2010
[21]

Yurov, Artyom V

Artyom V. Yurov, Artyom V. Astashenok and Valerian A. Yurov, ”The Cosmological Models with Jump Discontinuities”,Eur. Phys. J. C78 (2018) 542

2018
[22]

A. Yu. Kamenshchik, ”Quantum cosmology and late-time singularities”, Class. Quant. Grav.30(2013) 173001. 54

2013
[23]

Teodor Borislavov Vasilev, Mariam Bouhmadi-L´ opez, Prado Mart´ ın- Moruno, ”Classical and Quantumf(R) Cosmology: The Big Rip, the Little Rip and the Little Sibling of the Big Rip”, Universe7(2021) 8, 288

2021
[24]

Astashenok

A private correspondence with Artyom V. Astashenok
[25]

Concepts Phys

Andrei Linde, ”Particle Physics and Inflationary Cosmology”, Contemp. Concepts Phys. 5 (2005) 1–362

2005
[26]

V. F. Mukhanov and G. V. Chibisov, ”Quantum Fluctuation And ‘Non- singular’ Universe”, JETP Lett.33(1981) 549–553 [Pisma Zh. Eksp. Teor. Fiz. 33, 549 (1981)]

1981
[27]

S. W. Hawking, ”The Development Of Irregularities In A Single Bubble Inflationary Universe”, Phys. Lett. B 115 (1982) 295–297

1982
[28]

A. A. Starobinsky, ”Dynamics Of Phase Transition In The New In- flationary Universe Scenario And Generation Of Perturbations”, Phys. Lett. B 117 (1982) 175–178

1982
[29]

B. S. DeWitt, Phys. Rev. 160, 1113 (1967)

1967
[30]

J. A. Wheeler, in: Relativity, Groups, and Topology, edited by C. M. DeWitt and J. A. Wheeler, Benjamin, New York (1968)

1968
[31]

’t Hooft, ”Dimensional Reduction in Quantum Gravity”, ArXiv:gr- qc/9310026

G. ’t Hooft, ”Dimensional Reduction in Quantum Gravity”, ArXiv:gr- qc/9310026
[32]

Susskind, ”The World as a Hologram”, Journal of Mathematical Physics, 36 (1995) 6377–6396

L. Susskind, ”The World as a Hologram”, Journal of Mathematical Physics, 36 (1995) 6377–6396

1995
[33]

Bekenstein, ”Black Holes And The Second Law of Thermodynam- ics”, Lett

J.D. Bekenstein, ”Black Holes And The Second Law of Thermodynam- ics”, Lett. Nuovo Cim. 4 (1972) 737-740

1972
[34]

A Vilenkin, ”Creation of universes from nothing”,Physics Letters B117 (1982) 25–28

1982
[35]

Chernin, D.I

A.D. Chernin, D.I. Santiago, A.S. Silbergleit, ”The interplay between gravity and quintessence: a set of new GR solutions”,Physics Letters A 294(2002) 79–83. 55

2002
[36]

Frank J. Tipler, Jessica Graber, Matthew McGinley, Joshua Nichols- Barrer, Christopher Staecker, ”Closed universes with black holes but no event horizons as a solution to the black hole information problem”, Monthly Notices of the Royal Astronomical Society, Volume 379, Issue ...

2007
[37]

The Theory of the Universal Wavefunction (1955)

Hugh Everett “The Theory of the Universal Wavefunction (1955)”: In Bryce DeWitt, R. Neill Graham (eds.). “The Many-Worlds Interpreta- tion of Quantum Mechanics”,Princeton Series in Physics, Princeton University Press (1973), 3–140

1955
[38]

A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables (Parts I and II)

David Bohm, “A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables (Parts I and II)”,Phys. Rev.85(1952) 170–193

1952
[39]

The Large Scale Structure of Space- Time

Stephen Hawking, George Ellis, “The Large Scale Structure of Space- Time”, Cambridge University Press (1973)

1973
[40]

R. R. Caldwell, ”A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state”,Phys. Lett. B545(2002) 23–29

2002
[41]

R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, ”Phantom En- ergy and Cosmic Doomsday”,Phys. Rev. Lett.91(2003) 071301

2003
[42]

S. M. Carroll, M. Hoffman and M. Trodden, ”Can the dark energy equation-of-state parameterwbe less than -1?”,Phys. Rev. D68(2003) 023509

2003
[43]

P. F. Gonz´ alez-D´ ıaz, ”Achronal cosmic future”,Phys. Rev. Lett.93 (2004) 071301

2004
[44]

A. V. Yurov, P. M. Moruno and P. F. Gonz´ alez-D´ ıaz, ”New ”Bigs” in Cosmology”,Nucl. Phys. B759(2006) 320–341

2006
[45]

Gonz´ alez-D´ ıaz, Carmen L

Pedro F. Gonz´ alez-D´ ıaz, Carmen L. Siguenza, ”Phantom thermodynam- ics”,Nucl. Phys. B697(2004) 363–386

2004
[46]

Lima, J.S

J.A.S. Lima, J.S. Alcaniz, ”Thermodynamics, spectral distribution and the nature of dark energy”,Phys. Lett. B600(2004) 191–196. 56

2004
[47]

”Phantom scalar fields result in inflation rather than Big Rip”,Eur

Artyom Yurov, ”Phantom scalar fields result in inflation rather than Big Rip”, arXiv:astro-ph/0305019; Yurov, A.V. ”Phantom scalar fields result in inflation rather than Big Rip”,Eur. Phys. J. Plus126(2011) 132

2011 arXiv
[48]

A. V. Yurov, V. A. Astashenok, V. A. Yurov, ”The dressing procedure for the cosmological equations and the indefinite future of the universe”, Grav. Cosmol.14(2008) 8–16

2008
[49]

Jaume Garriga and Alexander Vilenkin, ”Many worlds in one”,Phys. Rev. D64(2001) 043511

2001
[50]

Andrei Linde, Vitaly Vanchurin, ”How many universes are in the mul- tiverse?”,Phys. Rev. D81(2010) 083525

2010
[51]

4 (1921) 217– 221

Edward Kasner, ”Geometrical Theorems on Einstein’s Cosmological Equations”,American Journal of Mathematics43No. 4 (1921) 217– 221

1921
[52]

V. A. Belinskii, I.M. Khalatnikov, ”Effect of Scalar and Vector Fields on the Nature of the Cosmological Singularity”,Sov. Phys. JETP36 (1973) 591

1973
[53]

A. Yu. Kamenshchik, ”The problem of singularities and chaos in cos- mology”,Phys. Usp.53(2010) 301–309

2010
[54]

Quantum equilibrium and the origin of absolute uncertainty

D. D¨ urr, S. Goldstein and N. Zangh´ ı, “Quantum equilibrium and the origin of absolute uncertainty”.J. Stat. Phys.67, 843–907 (1992)

1992
[55]

The Quantum Theory of Motion: An Account of the De Broglie-Bohm Causal Interpretation of Quantum Mechanics

Peter R. Holland, “The Quantum Theory of Motion: An Account of the De Broglie-Bohm Causal Interpretation of Quantum Mechanics”, Cambridge University Press, Cambridge (1993)

1993
[56]

Quantum potential: Physics, Geom- etry and Algebra

Ignazio Licata Davide Fiscaletti, “Quantum potential: Physics, Geom- etry and Algebra”, AMC, Springer (2013)

2013
[57]

Parallel Universes

Max Tegmark, “Parallel Universes”, Science and Ultimate Reality: From Quantum to Cosmos (honoring John Wheeler’s 90th birthday), ed. J. D. Barrow, P.C.W. Davies C.L. Harper. Cambridge University Press (2003)

2003
[58]

The Multiverse Hierarchy

Max Tegmark, “The Multiverse Hierarchy”, Universe or Multiverse?, ed. B. Carr, Cambridge University Press (2007) 57

2007

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

M. J. W. Hall, D.-A. Deckert and H. M. Wiseman, ”Quantum phenom- ena modelled by interactions between many classical worlds”,Phys. Rev. X4(2014) 041013

work page 2014

[2] [2]

A. V. Yurov, V. A. Yurov, ”The day the universes interacted: quantum cosmology without a wave function”,Eur. Phys. J. C79(2019) 771

work page 2019

[3] [3]

Perturbations and Linearization Stability of Closed Friedmann Universes

John D. Barrow, ”Is the universe ill-posed?”, http://arxiv.org/abs/2003.14108v2

work page Pith review arXiv 2003

[4] [4]

Raphael Bousso and Leonard Susskind, ”Multiverse interpretation of quantum mechanics”,Phys. Rev. D85(2012) 045007

work page 2012

[5] [5]

Roger Penrose, ”Cycles of Time: An Extraordinary New View of the Universe”, Random House (USA) (2010)

work page 2010

[6] [6]

Sean Carroll, ”From Eternity to Here: The Quest for the Ultimate The- ory of Time”, Hardcover – January 7, (2010)

work page 2010

[7] [7]

Bouhmadi-Lopez, P

M. Bouhmadi-Lopez, P. F. Gonz´ alez-D´ ıaz and P. Martin- Moruno,”Worse than a big rip?”,Phys. Lett. B659(2008) 1–5

work page 2008

[8] [8]

A. V. Yurov, A. V. Astashenok and P.F. Gonz´ alez-D´ ıaz, ”Astronomical bounds on future big freeze singularity”,Grav. Cosmol.14No. 3 (2008) 205–212

work page 2008