On Quantum Creation of a Toroidal Universe

It may state two separate claims as one.

The authors of Refs.[7][8][9] interpret the wave function for this model as a tunneling wave function, which amounts to dropping the condition that the probability flux must enter superspace through non-singular configurations.

“The authors of Refs.[7][8][9] nonetheless interpret the wave function for this model as a tunneling wave function, which amounts to dropping the condition that the probability flux must enter superspace through non-singular configurations.”

• cites [7] Y.B. Zeldovich, A.A. Starobinsky, Quantum creation of a universe in a nontrivial topology. Sov. Astron. Lett. 10, 135 (1984)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [8] D.H. Coule, J. Martin, Quantum cosmology and open universes. Phys. Rev. D 61, 063501 (2000). arXiv:gr-qc/9905056 sourcePartly supported

  The Introduction (p. 1) defines the tunneling condition as allowing only outgoing modes, and Section III (p. 7) says the authors use the tunneling or Vilenkin state. The paper does not say that this drops a requirement for probability flux to enter superspace through non-singular configurations; instead, Section III (p. 8) says a regularity requirement favors the tunneling wavefunction. (LLM, conf=0.86)

  Experimental — accuracy not yet measured
• cites [9] A.D. Linde, Creation of a compact topologically nontrivial inflationary universe. JCAP 0410, 004 (2004). arXiv:hep-th/0408164 sourceDisputed

  Section B, “Quantum creation of a compact inflationary universe” (page unavailable), says the compact flat toroidal universe appears “from nothing” without tunneling and has no potential barrier. That is contrary to attributing a tunneling interpretation of this model’s wave function to Linde. The section discusses probability current, but does not say that a condition on flux entering superspace through non-singular configurations is dropped. (LLM, conf=0.86)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

It may state two separate claims as one.

For the case discussed here, H = H_v at all points, so the average over the whole of each geodesic equals H_v, and the theorem of Ref. [1] shows that these geodesics cannot have infinite length.

“For the case discussed here, H = H v at all points, so the average over the whole of each geodesic equals H v , so the theorem of Ref. [1] shows that these geodesics cannot have infinite length.”

• cites [1] A. Borde, A.H. Guth, A. Vilenkin, Inflationary space-times are incomplete in past directions. Phys. Rev. Lett. 90, 151301 (2003). arXiv:gr-qc/0110012 sourceSupported

Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

The wave function (67) does not oscillate, hence the semiclassical description breaks down at small a.

“Coule & Martin [8] and Linde [9] note that the wave function (67) does not oscillate; hence the semiclassical description breaks down at small a.”

• cites [8] D.H. Coule, J. Martin, Quantum cosmology and open universes. Phys. Rev. D 61, 063501 (2000). arXiv:gr-qc/9905056 sourcePartly supported

  In II. DESCRIPTION OF THE MODEL (p. 4), the paper describes a nonoscillatory, exponentially decaying wavefunction at small a for the closed (k = 1) case. But the same section (p. 5) says the flat and open cases oscillate even before a reaches a₀. The source therefore supports the observation only for the closed case; it does not establish the claim for the citing paper’s wave function (67) or state that its semiclassical description breaks down. (LLM, conf=0.82)

  Experimental — accuracy not yet measured
• cites [9] A.D. Linde, Creation of a compact topologically nontrivial inflationary universe. JCAP 0410, 004 (2004). arXiv:hep-th/0408164 sourceSupported

Probably not a substantial claim.

Zeldovich and Starobinsky state that for massless conformally coupled fields in a toroidal universe described by the metric (57) with the stated identifications, the Casimir contribution to the energy-momentum tensor has the form T^(C)μν = -(C/a^4) diag(1, -1/3, -1/3, -1/3).

“Zeldovich and Starobinsky (ZS), citing Refs.[12,[35][36][37][38], state that for massless conformally coupled fields in a toroidal universe described by the metric (57) with the stated identifications, the Casimir contribution to the energymomentum tensor has the form”

• cites [12] B.S. DeWitt, Quantum theory of gravity. 1. The canonical theory. Phys. Rev. 160, 1113 (1967) sourceNot checked — no full text of the source
• cites [35] J.J. Blanco-Pillado, H.S. Ramadhan, B. Shlaer, Bubbles from Nothing. JCAP 1201, 045 (2012). (arXiv:1104.5229 [gr-qc]) sourceCould not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

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• cites [36] J. Feldbrugge, J. L. Lehners and N. Turok, Lorentzian Quantum Cosmology. Phys. Rev. D 95(10), 103508 (2017). https://doi.org/10.1103/PhysRevD.95.103508 (arXiv:1703.02076 [hep-th]) sourceCould not verify

  The Introduction discusses a closed-universe model and Lorentzian path integrals, not Casimir energy in a toroidal universe. Searches for Zeldovich and Starobinsky, conformally coupled fields, and the stated energy-momentum tensor found no passage addressing the claim in our copy. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

Ref.[37] gives the numerical value of C_0 as 0.833, but the paper also contains an analytic formula.

“In particular, Ref.[37] gives it as 0.833, but the paper also contains an analytic formula, found as a special case of”

• cites [37] J. Feldbrugge, J. L. Lehners and N. Turok, No smooth beginning for spacetime. Phys. Rev. Lett. 119(17), 171301 (2017) https://doi.org/10.1103/PhysRevLett.119.171301 (arXiv:1705.00192 [hep-th]) sourceCould not verify

  The passages from “No smooth beginning for spacetime” (page unavailable) give analytic expressions for cosmological amplitudes and perturbations, but none identifies a quantity C₀ or gives it the value 0.833. Searches for “0.833,” “C_0,” and an analytic expression for that coefficient found no passage addressing the claim. (LLM, conf=0.75)

  Experimental — accuracy not yet measured

Probably not a substantial claim. The paper’s conclusions may not depend on it.

The Hawking-Turok instanton can be obtained as a 4D section of a non-singular instanton in 5 dimensions.

“It has been shown in Refs.[43] and[44] that the Hawking-Turok instanton can be obtained as a 4D section of a non-singular instanton in 5 dimensions.”

• cites [43] A. Vilenkin and M. Yamada, Tunneling wave function of the universe.Phys. Rev. D 98(6), 066003 (2018). https://doi.org/10.1103/PhysRevD.98.066003(arXiv: 1808.02032 [gr-qc]) sourceCould not verify

  The Introduction and §3.1 discuss tunneling wave functions and four-dimensional de Sitter paths, but neither addresses the Hawking–Turok instanton as a section of a nonsingular five-dimensional instanton. Searches for “Hawking-Turok” and the four-/five-dimensional instanton description found no passage supporting that claim. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [44] A. Vilenkin and M. Yamada, Tunneling wave function of the universe II: the backreaction problem. Phys. Rev. D 99(6), 066010 (2019). https://doi.org/10.1103/PhysRevD.99.066010 (arXiv: 1812.08084 [gr-qc]) sourceCould not verify

  The Introduction discusses the tunneling wave function, and the Summary and Discussion describes four-dimensional saddle points; neither addresses the Hawking–Turok instanton as a section of a nonsingular five-dimensional instanton. Searches for “Hawking-Turok instanton” and “non-singular instanton in 5 dimensions 4D section” found no passage establishing the claim. The indexed passages provide no page numbers. (LLM, conf=0.75)

  Experimental — accuracy not yet measured

Probably not a substantial claim. The paper’s conclusions may not depend on it.

In 2002, Hawking and Hertog introduced a 'top-down approach,' a form of the weak anthropic principle, to solve this problem.

“In 2002, Hawking and Hertog[22] introduced a”

• cites [22] J. Hong, A. Vilenkin, S. Winitzki, Creation of massive particles in a tunneling universe. Phys. Rev. D 68, 023521 (2003). arXiv:gr-qc/0305025 sourceCould not verify

  The Introduction discusses particle creation during cosmological tunneling, and the Discussion describes a Gaussian vacuum; neither addresses a top-down approach or the weak anthropic principle. Searches for Hawking and Hertog, “top-down approach,” and “anthropic principle” found no relevant passage in our copy. The printed citation [22] appears beside Hawking and Hertog, but our copy does not establish what that citation identifies. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

It may state two separate claims as one.

For a spin-1/2 field with antiperiodic boundary conditions, C_{1/2} = 0.3914, so there is no cancellation.

“On the other hand, for a spin-1/2 field with antiperiodic boundary conditions, as studied in Ref. [39], ZS state that C 1/2 = 0.3914, so there is no cancellation.”

• cites [39] J. Diaz Dorronsoro, J. J. Halliwell, J. B. Hartle, T. Hertog and O. Janssen, Real no-boundary wave function in Lorentzian quantum cosmology. Phys. Rev. D 96(4), 043505 (2017). https://doi.org/10.1103/PhysRevD.96.043505 (arXiv:1705.05340 [gr-qc]) sourceCould not verify

  Section III (Scalar Matter; page unavailable) studies a scalar field, not a spin-1/2 field with antiperiodic boundary conditions. Searches for that field and boundary condition, cancellation, and 0.3914 found no passage in our copy addressing the attributed claim. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

The Hartle-Hawking wave function might evolve into eternal inflation, which is believed to generically lead to predictions that are independent of the initial state.

“Alternatively, the Hartle-Hawking wave function might evolve into eternal inflation, which is believed to generically lead to predictions that are independent of the initial state[23,24].”

• cites [23] S.J. Wang, M. Yamada, A. Vilenkin, Constraints on non-minimal coupling from quantum cosmology. JCAP 08, 025 (2019) sourceCould not verify

  The Introduction identifies the Hartle–Hawking no-boundary proposal, and §3.5 analyzes its wave function. Neither passage says that it might evolve into eternal inflation or that eternal inflation yields predictions independent of the initial state. Searches for those claims in our copy found no passage addressing them. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [24] J.E. Lesnefsky, D.A. Easson, P.C.W. Davies, Past-completeness of inflationary spacetimes. Phys. Rev. D 107(4), 044024 (2023). (arXiv:2207.00955 [gr-qc]) sourceCould not verify

  The Introduction (p. 4) discusses models of eternal inflation, and the Conclusion (p. 14) discusses stability under perturbations of initial conditions. Neither passage addresses whether the Hartle–Hawking wave function can evolve into eternal inflation or whether eternal inflation yields predictions independent of the initial state. Searches for those specific points found no supporting passage in our copy. (LLM, conf=0.74)

  Experimental — accuracy not yet measured

Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

Singular instantons in quantum cosmology have been discussed by Hawking and Turok [41], but it was argued in Ref. [42] that such instantons are not actually stationary points of the Euclidean action, since they fail to satisfy the equations of motion at the singular point.

“Singular instantons in quantum cosmology have been discussed by Hawking and Turok [41], but it was argued in Ref. [42] that such instantons are not actually stationary points of the Euclidean action, since they fail to satisfy the equations of motion at the singular point.”

• cites [41] J. Feldbrugge, J. L. Lehners and N. Turok, No rescue for the no boundary proposal: Pointers to the future of quantum cosmology. Phys. Rev. D 97(2), 023509 (2018) https://doi.org/10.1103/PhysRevD.97.023509 (arXiv:1708.05104 [hep-th]) sourceCould not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured
• cites [42] J. Diaz Dorronsoro, J. J. Halliwell, J. B. Hartle, T. Hertog, O. Janssen and Y. Vreys, Damped perturbations in the no-boundary state. Phys. Rev. Lett. 121(8), 081302 (2018). https://doi.org/10.1103/PhysRevLett.121.081302 (arXiv: 1804.01102 [gr-qc]) sourceCould not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

It may state two separate claims as one.

There is an infinity of solutions corresponding to different values of k_i, and the outgoing wave condition does not give preference to any of them.

“There is an infinity of solutions corresponding to different values of k i , and the outgoing wave condition does not give preference to any of them.”

It may state two separate claims as one.

A finite bound on the integral of H along a null or non-comoving past-directed geodesic was proved, so if the length of the geodesic were infinite, then H_av would have to be zero.

“We proved a finite bound on the integral of H along a null or non-comoving past-directed geodesic, so if the length of the geodesic were infinite, then H av would have to be zero.”

It may state two separate claims as one.

In the spherical de Sitter model, the constraint determines B_n = 0 for all n, selecting the conformal vacuum, which is the same as the Bunch-Davies state.

“Hence ζ m = ζ(a=0) = ∞, and the constraint (55) determines the values of B n uniquely: B n = 0 for all n.This selects the conformal vacuum, where the (negativefrequency) mode functions u n (η) are conformally related to the corresponding Minkowski space mode functions.For the de Sitter model this is the same as the Bunch-Davies state.”

It may state two separate claims as one.

In the perturbative superspace toroidal model, the Wheeler-DeWitt potential U(a) is negative for all values of a, so the entire range of a is classically allowed.

“The main difference is that the WDW potential U (a) is now negative for all values of a, and thus the entire range of a is classically allowed.”

It may state two separate claims as one.

In contrast to a spherical universe, there is no barrier to penetrate in the toroidal universe, so there is no tunneling suppression factor.

“In contrast to a spherical universe, there is no barrier to penetrate, so there is no tunneling suppression factor.”

It may state two separate claims as one.

The past boundary defined by t → -∞ in the toroidal model exhibits geodesic incompleteness and is therefore singular.

“Thus, the past boundary defined by t → -∞ exhibits geodesic incompleteness, and is therefore singular in the sense of Ref. [34].”

• cites [34] J. Garriga, Smooth ‘creation’ of an open universe in five-dimensions. arXiv:hep-th/9804106Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

It may state two separate claims as one.

The Casimir energy-momentum tensor is traceless and covariantly conserved.

“Note that it is traceless and covariantly conserved: T (C)ν ν = 0, T (C)ν µ;ν = 0.”

It may state two separate claims as one.

In the spherical model, the quadratic and higher order curvature corrections are negligible, and the curvature radius of the instanton is everywhere large compared to 1.

“In particular, the quadratic and higher order curvature corrections are negligible in this case.The curvature radius of the instanton is H -1 v and is everywhere large compared to 1.”

It may state two separate claims as one.

The instanton describing the tunneling in the Casimir case is singular at a = 0, with the total energy of the universe diverging as a → 0.

“First, the instanton describing the tunneling is singular at a = 0, with the total energy of the universe actually diverging as a → 0.”

Probably not a substantial claim. The paper may give no reason why it holds. The quote only partly states this claim.

The constant C can be estimated as C ≲ N, where N is the number of quantum fields in the model.

“The constant C can be estimated as”

The quote only partly states this claim.

The Friedmann equation with Casimir energy has a bouncing solution a(t) = a_min cosh^{1/2}(2H_v t) with a_min = (C/(3H_v^2))^{1/4}.

“This has a 'bouncing' solution”

Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.

Eq. (4) becomes C_0 = π^2/90 + ζ(3)/(2π) + π/6, which evaluates as 0.8246.

“Eq. ( 4), which becomes C 0 = π 2 90 + ζ(3) 2π + π 6 , which evaluates as 0.8246.”

Probably not a substantial claim. The paper may give no reason why it holds.

In the nucleation of a spherical universe, the total energy of matter vanishes in the limit a → 0.

“This situation should be contrasted with the nucleation of a spherical universe, in which case the total energy of matter vanishes in the limit a → 0.”

Probably not a substantial claim. The paper’s conclusions may not depend on it.

These Casimir energy calculations apply to a static universe.

“We also note that these Casimir energy calculations apply to a static universe.”

It may state two separate claims as one.

The turning point of the potential is at a = a_min, and the range 0 < a < a_min is classically forbidden.

“The turning point of the potential is at a = a min , and the range 0 < a < a min is classically forbidden.”

It may state two separate claims as one. The quote only partly states this claim.

The total Casimir energy in a toroidal universe is E(a) = -C/a, which approaches -∞ as a → 0.

“The total Casimir energy in a toroidal universe is”

It may state two separate claims as one.

For H_v ≪ 1 and C not too large, ζ_m ≫ 1, and the bound restricts the values of B_n to a narrow range around zero but does not determine them completely.

“For H v ≪ 1 and C not too large, we have ζ m ≫ 1.Then the bound (91) restricts the values of B n to a narrow range around zero, but it does not determine them completely.”

Probably not a substantial claim. It may state two separate claims as one.

In the limit C → 0+, ζ_m → ∞, which means that the quantum state is uniquely determined.

“If we consider the limit in which the Casimir energy approaches zero from above, C → 0+, Eq. ( 92) implies that ζ m → ∞, which means that the quantum state is uniquely determined.”

It may state two separate claims as one.

Analytic continuation of Eq. (77) gives a(τ) = a_min sin^{1/2}(2H_v τ), and at small τ, a(τ) ∝ τ^{1/2}, resulting in a curvature singularity.

“Analytic continuation of Eq. (77) gives a(τ”

It may state two separate claims as one.

In the full de Sitter space, the flat slicing covers only half the manifold, and any non-comoving backward-going timelike trajectory reaches t = -∞ in a finite amount of proper time; the periodic identifications cannot change that.

“In the full de Sitter space, the flat slicing covers only half the manifold, and any non-comoving backward-going timelike trajectory reaches t = -∞ in a finite amount of proper time.The periodic identifications cannot change that.”

• AssumptionThe authors state this as an assumption: The toroidal universe can be described as de Sitter space in a spatially flat coordinate system with periodic identifications.

The quote only partly states this claim.

The Wheeler-DeWitt equation for the perturbative superspace model with Casimir energy has the form of Eq. (32) with U(a) = (6H_v)^2(a_min^4 - a^4).

“The WDW equation for the perturbative superspace model has the form of Eq. ( 32) with U (a) = (6H v ) 2 (a 4 min -a 4 ),”

It may state two separate claims as one. The quote only partly states this claim.

The under-barrier Euclidean action is |S_E| = A(C/3/H_v^2)^{1/4} with A ≈ 4.6, in agreement with ZS.

“The under-barrier Euclidean action is”

• cites [7] Y.B. Zeldovich, A.A. Starobinsky, Quantum creation of a universe in a nontrivial topology. Sov. Astron. Lett. 10, 135 (1984)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The quote only partly states this claim.

The regularity condition imposes the constraint |B_n| ≤ e^{-2ω_n ζ_m} on the constants B_n.

“the regularity condition imposes the following constraints on the constants B n :”

Probably not a substantial claim.

The analyses of toroidal universes in Refs.[7], [8], and [9] were based on the tunneling approach.

“The analyses of toroidal universes in Refs.[7], [8], and [9] were based on the tunneling approach; hence we shall adopt the tunneling boundary condition in the present paper.”

• cites [7], [8], and [9]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim.

The criticisms of the theorem in Ref. [33] were based on a misunderstanding of the theorem.

“The theorem proven in Ref. [1] was recently disputed by Ref. [33], but those criticisms were based on a misunderstanding of the theorem.”

• cites [33] A. Vilenkin, Singular instantons and creation of open universes. Phys. Rev. D 57, 7069 (1998). arXiv:hep-th/9803084 sourceNot checked — no full text of the source

It may state two separate claims as one.

The quantum creation of a toroidal universe from nothing is either impossible or depends essentially on Planck-scale physics.

“We conclude that the quantum creation of a toroidal universe from nothing cannot be described in the context of semiclassical quantum gravity -it is either impossible, or it depends essentially on Planck-scale physics.”

• Also stated in: § 1 Introduction · plain

  “We argue that the quantum creation of a toroidal universe from nothing cannot be described in the context of semiclassical quantum gravity, and therefore it is either impossible or is essentially dependent on Planck-scale physics.”

Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

Both the Hartle-Hawking and the tunneling boundary conditions can only be implemented in the semiclassical approximation.

“It should be noted that, at the present level of understanding, both the Hartle-Hawking and the tunneling boundary conditions can only be implemented in the semiclassical approximation.”

It may state two separate claims as one.

A singularity could produce a Friedmann-Robertson-Walker universe that matches our observed universe, but it could also produce anything else.

“A singularity could produce a Friedmann-Robertson-Walker universe that matches our observed universe, but it could also produce anything else.”

It may state two separate claims as one.

The classical toroidal model describes a universe starting at a singularity and does not address the problem of the initial conditions.

“The classical toroidal model therefore describes a universe starting at a singularity and does not seem to address the problem of the initial conditions.”

It may state two separate claims as one.

The only constraint from the regularity condition in the perturbative superspace toroidal model is given by Eq. (53), which means that the quantum state of the field is largely unconstrained.

“The only constraint from the regularity condition is therefore given by Eq. ( 53), which means that the quantum state of the field is largely unconstrained.”

It may state two separate claims as one.

ZS give the coefficient C for a real scalar field as C_0 = 0.8375, for a vector field C_1 = 2C_0, and for a chiral spin-1/2 field with periodic boundary conditions C_{1/2} = -C_0.

“ZS give the coefficient C for a real scalar field as C 0 = 0.8375, for a vector field C 1 = 2C 0 , and for a chiral spin-1/2 field with periodic boundary conditions C 1/2 = -C 0 .”

• cites [7] Y.B. Zeldovich, A.A. Starobinsky, Quantum creation of a universe in a nontrivial topology. Sov. Astron. Lett. 10, 135 (1984)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

It may state two separate claims as one.

Any classical cosmological model beginning at a singularity can be recast in the form of a WKB wave function, but this does not bring us any closer to determining the initial state of the universe.

“In fact, any classical cosmological model beginning at a singularity can be recast in the form of a WKB wave function, but this does not bring us any closer to determining the initial state of the universe.”

It may state two separate claims as one.

This toroidal spacetime describes a classical universe originating at a singularity, and not a quantum origin.

“We argue that this spacetime describes a classical universe originating at a singularity, and not a quantum origin.”

• Also stated in: § 1 Introduction · plain

  “In the present paper we re-examine this issue and argue that the toroidal universe describes a classical universe originating at a singularity, and not a quantum origin.”

• AssumptionRests on an assumption: A classical universe originating at a singularity is not a quantum origin.

It may state two separate claims as one.

The covering space of the toroidal model, described by metric (57) without toroidal identification, is simply half of de Sitter space and is known to be past geodesically incomplete: all past-directed geodesics, except comoving timelike geodesics x_i = const, reach t = -∞ in a finite proper time.

“We consider first the covering space, described by the metric (57) without toroidal identification.This covering space is simply half of de Sitter space and is known (see, for example, Hawking & Ellis, Ref. [34], pp.125-126) to be past geodesically incomplete: all past-directed geodesics, except 'comoving' timelike geodesics x i = const, reach t = -∞ in a finite proper time.”

• cites Hawking & Ellis, Ref. [34]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim.

Quantum cosmology suggests that a spatially compact universe can spontaneously nucleate out of 'nothing'.

“Perhaps the most promising approach to this problem is based on quantum cosmology, which suggests that a spatially compact universe can spontaneously nucleate out of 'nothing', where 'nothing' refers to a state with no classical space, time, or matter [2][3][4][5][6][7].”

• cites [2] A. Vilenkin, Creation of universes from nothing. Phys. Lett. B 117, 25 (1982) sourceNot checked — no full text of the source
• cites [3] J.B. Hartle, S.W. Hawking, Wave function of the universe. Phys. Rev. D 28, 2960 (1983) sourceNot checked — no full text of the source
• cites [4] A.D. Linde, Quantum creation of the inflationary universe. Lett. Nuovo Cim. 39, 401 (1984) sourceNot checked — no full text of the source
• cites [5] V.A. Rubakov, Quantum mechanics in the tunneling universe. Phys. Lett. B 148, 280 (1984) sourceNot checked — no full text of the source
• cites [6] A. Vilenkin, Quantum creation of universes. Phys. Rev. D 30, 509 (1984) sourceNot checked — no full text of the source
• cites [7] Y.B. Zeldovich, A.A. Starobinsky, Quantum creation of a universe in a nontrivial topology. Sov. Astron. Lett. 10, 135 (1984)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

It may state two separate claims as one.

In Ref. [33], the authors restated the past-completeness condition as the mere requirement that the average value of H along any finite segment of the geodesic be strictly positive, which leads to a false statement for which they constructed counter-examples.

“In Ref. [33], however, the authors restated this condition (see Theorem 1 of that paper) as the mere requirement that the average value of H along any finite segment of the geodesic has to be strictly positive, which leads to a false statement to which they constructed counter-examples.”

• cites [33] A. Vilenkin, Singular instantons and creation of open universes. Phys. Rev. D 57, 7069 (1998). arXiv:hep-th/9803084 sourceNot checked — no full text of the source

Probably not a substantial claim. It may state two separate claims as one.

The Hartle-Hawking wave function predicts that the universe is most likely to nucleate with the lowest value of V(φ), which is not favorable for inflation.

“In contrast to the tunneling wave function, the Hartle-Hawking wave function predicts that the universe is most likely to nucleate with the lowest value of V (ϕ) [3], which is not favorable for inflation.”

• cites [3] J.B. Hartle, S.W. Hawking, Wave function of the universe. Phys. Rev. D 28, 2960 (1983) sourceNot checked — no full text of the source

It may state two separate claims as one.

Anything can collapse into a singularity, and since classical general relativity is time-reversal invariant, anything can emerge from a singularity.

“Anything can collapse into a singularity, and since classical general relativity is time-reversal invariant, anything can emerge from a singularity.”

It may state two separate claims as one.

The range 0 < a < a_min is classically forbidden due to the negative Casimir energy, but the universe can tunnel through this barrier.

“The range 0 < a < a min is classically forbidden, due to the negative Casimir energy, but the universe can tunnel through this barrier.”

It may state two separate claims as one.

Such quantum creation is either completely impossible, or could take place through Planck-scale processes beyond our current understanding.

“Such quantum creation is either completely impossible, or perhaps it could take place through Planck-scale processes beyond our current understanding.”

It may state two separate claims as one.

The curvature singularity implies that the instanton does not satisfy the equations of motion at a = 0, which means it is not a valid stationary point of the Euclidean action.

“The curvature singularity implies that the instanton does not satisfy the equations of motion at a = 0, which in turn means that it is not a valid stationary point of the Euclidean action.”

Probably not a substantial claim. The paper’s conclusions may not depend on it.

Ref. [42] points out that if such singular instantons were treated as valid stationary points, then it would be possible to construct a singular instanton which would lead to the rapid decay of flat space.

“Ref. [42] also points out that if such singular instantons were treated as valid stationary points, then it would be possible to construct a singular instanton which would lead to the rapid decay of flat space.”

• cites [42] J. Diaz Dorronsoro, J. J. Halliwell, J. B. Hartle, T. Hertog, O. Janssen and Y. Vreys, Damped perturbations in the no-boundary state. Phys. Rev. Lett. 121(8), 081302 (2018). https://doi.org/10.1103/PhysRevLett.121.081302 (arXiv: 1804.01102 [gr-qc]) sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

It may state two separate claims as one.

The toroidal universe describes nothing more than a classical universe originating at a singularity, and not a quantum origin of the universe.

“In this paper we argued that the toroidal universe describes nothing more than a classical universe originating at a singularity, and not a quantum origin of the universe.”

Probably not a substantial claim. The paper’s conclusions may not depend on it.

The Casimir energy vanishes in supersymmetric models, where N_b = N_f.

“ZS note that the Casimir energy vanishes in supersymmetric models, where N b = N f .”

• cites [7] Y.B. Zeldovich, A.A. Starobinsky, Quantum creation of a universe in a nontrivial topology. Sov. Astron. Lett. 10, 135 (1984)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

It may state two separate claims as one.

The width of the allowed range of B_n decreases exponentially towards larger values of ω_n, so the allowed states may be observationally indistinguishable from the Bunch-Davies state.

“The width of the allowed range of B n decreases exponentially towards larger values of ω n , so the allowed states may be observationally indistinguishable from the Bunch-Davies state.”

Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

Saharian and Mkhitaryan carried out the corresponding Casimir calculation for a power-law expanding universe, with a(t) ∝ t^p, and found that it agrees with the static calculation in the limit of small a.

“Saharian and Mkhitaryan [40] carried out the corresponding calculation for a power-law expanding universe, with a(t) ∝ t p , and found, as one would expect, that it agrees with the static calculation in the limit of small a.”

• cites [40] J. Feldbrugge, J. L. Lehners and N. Turok, Inconsistencies of the New No-Boundary Proposal. Universe 4(10), 100 (2018). https://doi.org/10.10.3390/universe4100100 (arXiv: 1805.01609 [hep-th]) sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.