Stealth branes

It may state two separate claims as one.

From the bulk point of view, stealth branes have vanishing energy and momentum, and their nucleation is not forbidden by any conservation laws.

“From the point of view of the bulk, stealth branes have vanishing energy and momentum, and their nucleation is not forbidden by any conservation laws.”

The quote only partly states this claim.

If the bulk cosmological constant vanishes and the brane has a nonzero mass M+ ≡ M ≠ 0 with M- = 0, then for sufficiently large brane radii the left-hand side of Eq. (49) yields a correction to stealth evolution due to the non-zero brane mass.

“The second term in the brackets represents a correction to the stealth evolution due to a non-zero brane mass.”

• AssumptionThe authors state this as an assumption: The bulk energy-momentum tensor has the vacuum form T±AB = -k^{-1} Λ± gAB.

It may state two separate claims as one.

The characteristic amplitude of zero-point brane fluctuations on a length scale L is Y_a ∼ ρ_v^{-1/2} L^{-1}; the brane can be treated as a well-localized classical object as long as Y_a ≪ L, i.e., on scales L ≫ ρ_v^{-1/4}.

“This gives Y a ∼ ρ -1/2 v L -1 (59 ) The brane can be treated as a well-localized classical object as long as Y a ≪ L, that is, on scales L ≫ ρ -1/4 v .”

It may state two separate claims as one.

A stealth brane corresponds to M± = 0 and Λ+ = Λ- ≡ Λ; in this case the junction equations reduce to the standard FRW evolution equations, and even a non-zero bulk cosmological constant has no effect on the brane evolution.

“A stealth brane corresponds to M ± = 0 and Λ + = Λ -≡ Λ.As expected, in this case Eqs.(49), (50) reduce to the standard FRW evolution equations.Even if the bulk cosmological constant is non-zero, it has no effect on the evolution of the brane.”

• AssumptionThe authors state this as an assumption: The bulk energy-momentum tensor has the vacuum form T±AB = -k^{-1} Λ± gAB.

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

Quanta of the fields Y_a can be copiously created in particle collisions; the effective coupling at energy ε is λ_eff ∼ ε^4/ρ_v, so the theory becomes strongly interacting at energies ε >~ ρ_v^{1/4}.

“The effective coupling constant at energy ǫ is λ ef f ∼ ǫ 4 /ρ v , so the theory becomes strongly interacting at energies ǫ > ∼ ρ 1/4 v .”

It may state two separate claims as one.

In a model with a flat 4D brane world in two extra dimensions, the brane evolution equation is trivially satisfied for K^iμν = 0, and the bulk Einstein equations are solved by a conical metric; the bulk metric is locally flat and stealth brane nucleation proceeds as in flat spacetime.

“The brane evolution equation ( 16) is trivially satisfied for K i µν = 0, and the bulk Einstein's equations ( 13) are solved by a conical metric in the extra dimensions.The bulk metric is then locally flat, and stealth brane nucleation will proceed as in flat spacetime.”

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

The Hartle-Hawking wave function gives P_HH ∝ exp(-S(E)), while the tunneling and Linde wave functions give P_T ∝ exp(-|S(E)|).

“The Hartle-Hawking [25] wave function gives P HH ∝ exp(-S (E) ) ,(20) while the tunneling [27,28] and Linde [26] wave functions give P T ∝ exp(-|S (E) |) .(21)”

• cites [25]Not matched

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• cites [27]Not matched

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• cites [28]Not matched

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• cites [26]Not matched

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It may state two separate claims as one.

The nucleation rate of stealth branes is described by the same 4-sphere instanton as in 4D quantum cosmology, now embedded in a Minkowski bulk, and the bulk does not contribute to the instanton action.

“One can expect that the nucleation rate is described by the same 4-sphere instanton, which is now embedded in a Minkowski bulk.The bulk does not contribute to the instanton action, so the action is also the same,”

It may state two separate claims as one.

For stealth branes, the bulk gravitational field is absent and the Davidson et al. model is an appropriate minisuperspace approximation.

“For stealth branes in our model, the bulk gravitational field is absent and the model of [31,32] is an appropriate minisuperspace approximation.”

• cites [31]Not matched

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

• cites [32]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 the brane nucleation process, newly created branes expand and no contracting branes are present; therefore the tunneling wave function (or its complex conjugate) is the only correct choice.

“In the brane nucleation process, the newly created branes expand and no contracting branes are present.Thus the tunneling wave function (31) (or its complex conjugate) is the only correct choice in this case.”

• AssumptionThe authors state this as an assumption: Factor ordering ambiguities in the Wheeler-DeWitt equation are disregarded.

It may state two separate claims as one.

For N ≥ 10, any 4D Universe can be embedded at least locally, and for N ≥ 91 a global embedding is also possible.

“For N ≥ 10, any 4D Universe can be embedded at least locally [21], and for N ≥ 91. a global embedding is also possible [22].”

• cites [21]Not matched

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• cites [22]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.

Without Z2 symmetry, effective 4D gravity on the brane could still be obtained for weak sources, but this behaviour does not extend to strong gravitational fields or early Universe cosmology.

“Somewhat surprisingly, effective 4D gravity on the brane could still be obtained for weak sources [15,16], but this behaviour does not extend to strong gravitational fields or to the early Universe cosmology.”

• cites [15]Not matched

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

• cites [16]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 such a model, we may be living on a flat brane separating two anti-de Sitter regions, but stealth branes will nucleate and expand in the anti-de Sitter bulk; their internal geometry will be de Sitter with vacuum energy given by the brane tension.

“Then, we may be living on a flat brane separating two anti-de Sitter regions, but stealth branes will nucleate and expand in the anti-de Sitter bulk.Their internal geometry will be de Sitter, with the vacuum energy given by the brane tension.”

It may state two separate claims as one.

The degeneracy of brane evolution may be removed if only perturbatively stable stealth solutions are allowed; a brane that suddenly starts moving with finite acceleration is not perturbatively stable.

“The degeneracy of brane evolution may be removed if only perturbatively stable stealth solutions are allowed (that is, solutions which admit a full spectrum of infinitesimal perturbations).”

• Also stated in: § VI. CONCLUSIONS AND DISCUSSION · plain

  “Thus, a brane which suddenly starts moving with a finite acceleration is not perturbatively stable.”

Probably not a substantial claim.

Enforcing Z2 symmetry disallows stealth branes.

“One way around this problem is to enforce the Z 2 symmetry, thus disallowing stealth branes.”

It may state two separate claims as one.

To avoid excessive collisions of our brane with stealth branes in that model, one can introduce a small cosmological constant in the bulk, and brane collisions will be rare provided the brane nucleation rate is sufficiently low.

“To avoid an excessive rate of collisions of our brane with stealth branes, one can introduce a small cosmological constant in the bulk, and brane collisions will be rare, provided that the brane nucleation rate is sufficiently low.”

It may state two separate claims as one.

The existence of stealth branes indicates that the bulk space is unstable, and there is a danger that it may fill up with nucleated branes, so that brane inhabitants will be constantly bombarded by other branes hitting them from extra dimensions.

“The existence of stealth branes indicates that the bulk space is unstable, and there is a danger that it may fill up with nucleated branes, so that the brane inhabitants will be constantly bombarded by other branes hitting them from extra dimensions.”

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

For positive Λ, the static coordinates cannot be used beyond the de Sitter horizon a < H^{-1}, but since no singularities develop at a = H^{-1}, the solution for a(t) can be analytically continued so that standard evolution continues at a > H^{-1}.

“However, since no singularities are developed at a = H -1 , one can expect that the solution for a(t) will be analytically continued, so that the standard evolution will continue at a > H -1 .”

It may state two separate claims as one.

For N > 5, brane gravity is always 4D for zero-thickness branes, but crossover to higher-dimensional behaviour is recovered when finite thickness of the brane is taken into account.

“One finds that the brane gravity is always 4D for zero-thickness branes [7]. However, the crossover to a higher-dimensional behaviour is recovered when the finite thickness of the brane is taken into account.”

• cites [7]Not matched

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It may state two separate claims as one.

Apart from stealth branes, the model also allows branes with negative bulk energy, so one could have spontaneous creation of brane pairs, one with energy E1 > 0 and the other with E2 = -E1; alternatively, a positive energy brane can increase its energy by chopping off a negative energy brane.

“Apart from stealth branes, the model also allows the existence of branes with negative bulk energy.So one could have spontaneous creation of brane pairs, one with energy E 1 > 0 and the other with E 2 = -E 1 .Alternatively, a positive energy brane can increase its energy by chopping off a negative energy brane.”

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

The Schwarzschild solution can only be embedded for N ≥ 6.

“For example, the Schwarzschild solution can only be embedded for N ≥ 6 [23].”

• cites [23]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 quote only partly states this claim.

Expanding stealth branes will occasionally run into our brane, and constraints on model parameters can be derived by requiring such collisions to be sufficiently rare.

“and one can derive constraints on the model parameters by requiring that such brane collisions should be sufficiently rare.”

It may state two separate claims as one.

These models include the Randall-Sundrum-type 5D model with positive brane tension, negative bulk cosmological constant, and brane curvature term, with values tuned to allow nearly flat brane solutions; the original Z2 symmetry can be lifted as long as the bound (62) is satisfied.

“These models include the Randall-Sundrum-type 5D model with a positive brane tension ρ v , a negative bulk cosmological constant Λ, and a brane curvature term in the action.The values of ρ v and Λ are tuned to allow (nearly) flat brane solutions.The original Randall-Sundrum model assumed Z 2 symmetry, but it can be lifted, as long as (62) is satisfied.”

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

In the DGP model with a 5D bulk and Z2 symmetry, gravity on the brane is effectively 4D on scales r << r0 and becomes 5D on larger scales, with r0 = M4^2/(2 M5^3).

“Assuming a 5-dimensional bulk and a Z 2 symmetry of reflections with respect to the brane, they found that gravity on the brane is effectively 4D on scales r << r 0 , with r 0 = M 2 (4)2M 3 (5) , and becomes 5D on larger scales.”

• cites [5]Not matched

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It may state two separate claims as one.

If we live on a stealth brane, the tension of the brane is equal to the 4D cosmological constant, which is observationally constrained by ρ_v <~ (10^{-3} eV)^4.

“If we live on a stealth brane, then the tension of the brane is equal to the 4D cosmological constant.This is observationally constrained by ρ v < ∼ (10 -3 eV ) 4 .(56)”

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

In an expanding de Sitter bulk, branes will be driven apart by the exponential expansion of the bulk, and brane collisions will be rare provided the brane nucleation rate is sufficiently low.

“One could also consider an expanding de Sitter bulk.The branes will then be driven apart by the exponential expansion of the bulk, and brane collisions will be rare, provided that the brane nucleation rate is sufficiently low.”

It may state two separate claims as one.

The instanton describing stealth brane nucleation in de Sitter space is the same 4-sphere instanton as in Minkowski space, embedded into an N-sphere, and the rate of brane nucleation is unchanged.

“The instanton describing stealth brane nucleation in de Sitter space is the same 4-sphere instanton as in Minkowski space, except now it is embedded into an N-sphere (Euclideanized N-dimensional de Sitter space).The difference between the instanton action and the N-sphere action without a brane is still given by Eq. ( 18), so the rate of brane nucleation is also unchanged.”

It may state two separate claims as one.

With such extremely small tension, quantum fluctuations of the brane on small length scales would be unacceptably large, and scalar particles corresponding to these fluctuations would be copiously produced in high-energy particle collisions in accelerators.

“We are going to argue that with such extremely small tension, the quantum fluctuations of the brane on small length scales would be unacceptable large.Moreover, the scalar particles corresponding to these fluctuations would be copiously produced in highenergy particle collisions in accelerators.”