Out of the White Hole: A Holographic Origin for the Big Bang

The self-accelerating branch suffers from a negative energy ghost instability.

“However, as discussed in the introduction, SA branch suffers from a negative energy ghost instability.”

• cites [8] L. Pilo, 2000, J. High Energy Phys. sourcePartly supported

  The Introduction and §3 describe a negative-kinetic-term radion and an associated negative-energy instability in the GRS model. They do not identify a self-accelerating (SA) branch or establish that this branch has the instability; that condition is unsupported by this source. (LLM, conf=0.84)

  Experimental — accuracy not yet measured
• cites [9] M.A. Luty, 2003, J. High Energy Phys. sourceNot checked — no full text of the source
• cites [10] A. Nicolis, 2004, J. High Energy Phys. sourceSupported
• cites [11] C. Charmousis, 2006, J. High Energy Phys. sourceNot checked — no full text of the source

Observational constraints on the DGP normal branch r_c > 3H0^-1 translate into an upper limit on the 5D Planck mass H/M5 < (H0 M4^2 /6)^1/3 ∼ 9 MeV.

“To see this, we can translate the observational constraints on the DGP cosmology (normal branch), r c 3H -1 0 [14] into an upper limit on 5D Planck mass: H M 5 H 0 M 2 4 6 1/3 ∼ 9 MeV, (5.1)”

• cites [14] sourcePartly supported

  Section 5 (Results; page not available) reports observational constraints on the normal branch of the warped DGP model, and §2.1 identifies r_c as its crossover scale and relates it to the five-dimensional mass. The available non-abstract passages do not establish the specific bound r_c > 3H₀⁻¹. The conversion to approximately 9 MeV is presented as the citing authors’ calculation, rather than a result attributed directly to this source. (LLM, conf=0.72)

  Experimental — accuracy not yet measured

In the presence of adiabatic perturbations, independent Hubble patches differ only in their local value of comoving spatial curvature K.

“In the presence of adiabatic perturbations, which are currently consistent with all cosmological observations (e.g.[1,20]), these independent Hubble patches would only differ in their local value of comoving spatial curvature K.”

• cites [1] Planck collaborationNot matched

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

• cites [20] sourceCould not verify

  The FRW-universe and effective Friedmann-equations sections discuss homogeneous cosmology and a curvature term, but do not address independent Hubble patches or adiabatic perturbations. Searches for those concepts and for observational consistency found no passage supporting the attributed claim. (LLM, conf=0.74)

  Experimental — accuracy not yet measured

The transition scale r_c is constrained to be bigger than today's cosmological horizon scale.

“which is constrained to be bigger than today's cosmological horizon scale (e.g., [14]).”

• cites [14] sourceCould not verify

  The supplied passages contain no match, and further searches of our copy for the transition or crossover scale, r_c, Hubble radius, and cosmological horizon returned no passages. I cannot verify from our copy that the paper constrains r_c to exceed today’s cosmological horizon scale. (LLM, conf=0.68)

  Experimental — accuracy not yet measured

• AssumptionThe authors state this as an assumption: The induced fluid has always had a negligible contribution to cosmic expansion, with the possible exception of the pressure singularity.

The 4d Newtonian potential due to thermal fluctuations has a scale-invariant power spectrum of amplitude ∼ G_b T^3 ∼ (T/M5)^3.

“Therefore, Eq. (4.8) implies that the 4d Newtonian potential, due to thermal fluctuations, has a scale-invariant power spectrum of the amplitude of ∼ G b T 3 ∼ (T /M 5 ) 3 .”

Pairs highlighted with the orange plane are possible choices of parameters {Ω_k, r_h} that satisfy r3 ≥ r_h for -Ω_k ≤ 0.01 at a = 10^-10.

“Consequently the pairs highlighted with orange plane are possible choices of parameters {Ω k , r h } that satisfy r 3 ≥ r h for -Ω k ≤ 0.01 at a = 10 -10 .”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

A thermal atmosphere in equilibrium with the brane can lead to scale-invariant curvature perturbations at the level of cosmological observations, with little fine-tuning, if the temperature is ∼20% of the 5D Planck mass.

“Surprisingly, we found that a thermal atmosphere in equilibrium with the brane can lead to scale-invariant curvature perturbations at the level of cosmological observations, with little fine-tuning, i.e. if the temperature is ∼ 20% of the 5D Planck mass.”

• AssumptionThe authors state this as an assumption: At some point in its early cosmological evolution, the 3-brane was in static equilibrium with its thermal 4d atmosphere.

The pressure becomes singular at ρ = ρ_s.

“Equation (2.14) immediately implies that the pressure becomes singular at ρ = ρ s .”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

Both terms in the induced fluid density become much smaller than the matter density if ρ is much less than ρ_s.

“Specifically, it is easy to see that both terms in the induced fluid density, ρ (Eq.2.13), become much smaller than the matter density, ρ, if ρ ρs .”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

The slight deviation from scale-invariance in the observed spectrum, at the level of 4% and detected with Planck at >5σ, is not predicted in the simple model of thermal free 5D field theory.

“The slight deviation from scale-invariance in Eq. ( 4.3), which is at the level of 4%, and is now detected with Planck at > 5σ level, is not predicted in our simple model of thermal free 5D field theory.”

For any {Ω_k, r_h} under the green plane, r3 < r_h.

“Therefore, for any {Ω k , r h } under the green plane, we have r 3 < r h .”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

Using the thermal 2-point function, the density fluctuation correlator is given by Eq. (4.6).

“straightforward manipulations using Eq. ( 4.4) yield ρ(x)ρ(y) T 5 8”

• AssumptionThe authors state this as an assumption: The thermal gas of massless scalar particles is in (4+1)-dimensional flat spacetime.

For pairs {Ω_k, r_h} above the green plane, the radius of the holographic universe is larger than the horizon radius, meaning the present cosmos lies outside the black hole horizon in the bulk, i.e. r3 > r_h.

“For those pairs {Ω k , r h } chosen to be above this plane the radius of our holographic universe is larger than the horizon radius, meaning that our present cosmos lies outside the horizon of the black hole in the bulk, i.e. r 3 > r h .”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

Demanding reality of all quantities in (3.8) gives ρ_s ≥ 2(ρ_BH - ρ).

“One is from demanding reality of all quantities in (3.8), i.e. ρ s ≥ 2 (ρ BH -ρ) .”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

The simple model of cosmological perturbations developed in Sec. 4 is already ruled out by cosmological observations at >5σ level, as it does not predict any deviations from scale-invariance.

“As we pointed out, the simple model of cosmological perturbations, developed in Sec. 4 is already ruled out by cosmological observations at > 5σ level, as it does not predict any deviations from scale-invariance.”

Pairs {Ω_k, r_h} with -Ω_k ≤ 0.01 satisfying ρ_BH ρ_r(a = 10^-10), i.e. lying above the intersection of the red surface and the a = 10^-10 plane, are allowed.

“Hence those pairs {Ω k , r h } with -Ω k ≤ 0.01 satisfying ρ BH ρ r (a = 10 -10 ), i.e. lie above the intersection of the red surface and the a = 10 -10 plane are allowedfoot_0 .”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

For a thermal gas of massless scalar particles in (4+1)-dimensional flat spacetime, the thermal 2-point correlation function is given by the Bose-Einstein distribution.

“Let us first compute the power spectrum of density fluctuations for a thermal gas of massless scalar particles in (4+1)-dimensional flat spacetime.The thermal 2-point correlation function of a free scalar field is given in terms of the Bose-Einstein distribution:”

• AssumptionThe authors state this as an assumption: The thermal gas of massless scalar particles is in (4+1)-dimensional flat spacetime.

ρ_s sets the characteristic density scale below which bulk gravity becomes important.

“Furthermore, we note that ρs sets the characteristic density scale, below which the bulk gravity becomes important.”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

The Flatness Problem is addressed by assuming a large mass/energy for the 5D star M*.

“The Flatness Problem, which refers to the surprisingly small spatial curvature of our universe, is addressed by assuming a large mass/energy for the 5D”

• Also stated in: § 5 Summary and Discussions · plain

  “star”

• Also stated in: § 5 Summary and Discussions · plain

  “, M * .”

• AssumptionThe authors state this as an assumption: The 5D star has a large mass/energy M*.

Since nothing can escape the horizon of a black hole, pairs {Ω_k, r_h} whose corresponding blue lines cross the green plane at some a > 10^-10 are excluded.

“Since nothing can escape the horizon of a black hole, one would exclude those pairs of {Ω k , r h } for which their corresponding blue lines at some a > 10 -10 cross the green plane.”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

Because the holographic fluid is subdominant for most of cosmic evolution, standard cosmological perturbation theory is applicable.

“As the holographic fluid is sub-dominant for most of the cosmic evolution, one expects the standard cosmological perturbation theory, that has been extremely successful in explaining cosmic microwave background observations (e.g.[1,20], amongst other observational probes), to be applicable.”

• cites [1] Planck collaborationNot matched

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

• cites [20] sourceNot checked yet

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

The detailed predictions of the self-accelerating branch were inconsistent with cosmological observations.

“Furthermore, the detailed predictions of the SA branch were inconsistent with cosmological observations [13].”

• cites [13] sourceNot checked yet

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

Thermal fluctuations in the atmosphere of the 3-brane induce a near-scale-invariant spectrum of curvature perturbations on the cosmological brane.

“Here, we argue that the thermal fluctuations in the atmosphere of the 3-brane induce a near-scale-invariant spectrum of curvature perturbations (∼ Eq. 43) on our cosmological brane.”

• AssumptionThe authors state this as an assumption: The 3-brane has Z2 (mirror) boundary conditions.
• AssumptionThe authors state this as an assumption: The atmosphere is composed of bulk degrees of freedom stratified just outside the 3-brane due to the gravitational pull of the black hole.

The construction lives in an asymptotically flat space-time.

“Yet another attractive feature of our construction is that it lives in an asymptotically flat space-time.”

The singularity can never be created through evolution from smooth initial conditions.

“Therefore, it can never be created through evolution from smooth initial conditions.”

Crossing the green plane means that at some early time the radius of the universe was smaller than the horizon radius.

“Indeed, crossing the green plane means that at some early time the radius of the universe was smaller than the horizon radius.”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

The timescale for the Jeans instability can be significantly longer than the Hubble time, limiting its maximum growth.

“However, the timescale for the Jeans instability can be significantly longer than the Hubble time, thus limiting its maximum growth.”

The region inside a white hole horizon is to the future of a 4D white hole naked singularity.

“the region inside a white hole horizon is to the future of a 4D white hole naked singularity (Figure 3-right)”

• AssumptionThe authors state this as an assumption: Our universe is a (3+1)-dimensional holographic image, a brane, of a (4+1)-dimensional background Schwarzschild geometry.
• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

This yields an alternative holographic origin for the big bang, in which our universe emerges from the collapse of a 5D star into a black hole.

“This yields an alternative holographic origin for the big bang, in which our universe emerges from the collapse a 5D”

• Also stated in: § 5 Summary and Discussions · plain

  “star”

• Also stated in: § 5 Summary and Discussions · plain

  “into a black hole, reminiscent of an astrophysical core-collapse supernova (Fig. 3-left).”

The violation of causality from superluminal propagation in DGP is only a pathology for spacetimes that do not admit a consistent chronology for (super)luminal signals.

“However this violation of causality is only a pathology for spacetimes that don't admit a consistent chronology for (super)luminal signals [24].”

• cites [24] F. CachazoNot matched

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

Any thermal atmosphere for the brane, with comoving temperature of about 20% of the 5D Planck mass, can induce scale-invariant primordial curvature perturbations on the brane, circumventing the need for a separate process such as cosmic inflation to explain current cosmological observations.

“Furthermore, we outline a novel mechanism through which any thermal atmosphere for the brane, with comoving temperature of ∼ 20% of the 5D Planck mass can induce scale-invariant primordial curvature perturbations on the brane, circumventing the need for a separate process (such as cosmic inflation) to explain current cosmological observations.”

• AssumptionThe authors state this as an assumption: Our universe is a (3+1)-dimensional holographic image, a brane, of a (4+1)-dimensional background Schwarzschild geometry.
• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

The pressure singularity uncovered in prior work is generically encountered at early times as matter density decays more slowly than a^-4.

“Focusing on the pressure singularity uncovered in [15], we showed that it is generically encountered at early times as matter density decays more slowly than a -4 .”

• cites [15] R. Gregory, 2007, J. High Energy Phys. sourceNot checked — no full text of the source

Assuming Z2 boundary conditions at x4 = 0, comparison of the metrics implies ζ(x^i) = -Φ4(x^i, x4 = 0).

“Then a comparison of (4.2) and (4.7) implies that ζ(x i ) = -Φ 4 (x i , x 4 = 0) (4.12) assuming Z 2 boundary conditions at x 4 = 0.”

• AssumptionThe authors state this as an assumption: The 3-brane has Z2 (mirror) boundary conditions.
• AssumptionThe authors state this as an assumption: At some point in its early cosmological evolution, the 3-brane was in static equilibrium with its thermal 4d atmosphere.

In the white hole picture, the pressure singularity can be interpreted as a holographic description of the Big Bang that takes place at a < 10^-10.

“In this picture one may interpret the pressure singularity as a holographic description of the Big Bang that takes place at a < 10 -10 .”

• AssumptionThe authors state this as an assumption: Our universe is a (3+1)-dimensional holographic image, a brane, of a (4+1)-dimensional background Schwarzschild geometry.
• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

In the white hole scenario, the entire range of pairs {Ω_k, r_h} above the red surface is allowed.

“Therefore the entire range of pairs {Ω k , r h } above the red surface is allowed; the lowest blue line in Figure 2 illustrates one such possible scenario.”

• AssumptionThe authors state this as an assumption: Our universe is a (3+1)-dimensional holographic image, a brane, of a (4+1)-dimensional background Schwarzschild geometry.
• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

For superhorizon perturbations, locality and causality imply that one can use Friedmann equations with independent constants of motion within independent Hubble patches.

“For super horizon perturbations, general arguments based on locality and causality imply that one can use Friedmann equations with independent constants of motion, within independent Hubble patches.”

A detection of curvature should generically accompany a detection of large scale anisotropy, because a generic black hole has finite angular momentum that would distort FRW symmetry on the scale of the curvature.

“However, a detection curvature should generically accompany a detection of large scale anisotropy, as a generic black hole will have a finite angular momentum, which would distort FRW symmetry on the scale of the curvature.”

No pressure singularity could happen for pairs {Ω_k, r_h} chosen to be above the red plane at any given time.

“Consequently no pressure singularity could happen for pairs {Ω k , r h } chosen to be above the red plane at any given time.”

• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

The integration constant μ from Section 2 can be interpreted as the mass of the black hole in the bulk, given in terms of the horizon radius.

“Comparing (2.13) with (3.8) we see that the integration constant µ from the previous section could be interpreted as the mass of the black hole in the bulk, given in terms of the horizon radius as 11)”

• AssumptionThe authors state this as an assumption: Our universe is a (3+1)-dimensional holographic image, a brane, of a (4+1)-dimensional background Schwarzschild geometry.
• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).

The DGP braneworld model with both 4d induced and 5d bulk gravity has the feature that the universe emerges as a spherical 3-brane out of the formation of a 5d Schwarzschild black hole.

“We describe a braneworld description of cosmology with both 4d induced and 5d bulk gravity (otherwise known as Dvali-Gabadadze-Porati, or DGP model), which exhibits this feature: The universe emerges as a spherical 3-brane out of the formation of a 5d Schwarzschild black hole.”

• AssumptionThe authors state this as an assumption: Our universe is a (3+1)-dimensional holographic image, a brane, of a (4+1)-dimensional background Schwarzschild geometry.

The Horizon Problem is addressed because the 5D star that collapsed into a black hole could have had plenty of time to reach uniform temperature across its core.

“The Horizon Problem, which refers to the uniform temperature of causally disconnected patches, is addressed, as the”

• Also stated in: § 5 Summary and Discussions · plain

  “star”

• Also stated in: § 5 Summary and Discussions · hedged

  “that collapsed into a 5D black hole could have had plenty of time to reach uniform temperature across its core.”

In a white hole bulk scenario, it is possible for the universe to be inside the horizon at any time up to the present since all matter eventually emerges from the white hole horizon.

“With this scenario, it is possible for the universe to be inside the horizon at any time up to the present since all matter eventually emerges from the white hole horizon.”

• AssumptionThe authors state this as an assumption: Our universe is a (3+1)-dimensional holographic image, a brane, of a (4+1)-dimensional background Schwarzschild geometry.
• AssumptionThe authors state this as an assumption: The brane is dynamical and located at r = a(τ)/√K, described by the FRW metric (2.1).