Kevin Langhoff and colleagues in their recent paper studied the eternally inflating multiverse using the global spacetime approach.
The holographic principle is a property of quantum gravity theories which resolves the black hole information paradox within string theory. It states that a fundamental description of quantum gravity resides in a space-time, often non-gravitational, whose dimension is lower than that of the bulk spacetime.
An idea of holography can be implemented via two approaches. The first approach start from global spacetime of general relativity & identify independent quantum degrees of freedom using the quantum extremal surface (QES) prescription. Another approach starts with a description that is manifestly unitary and understand how the picture of global spacetime emerges.
Kevin Langhoff and colleagues in their recent paper studied the eternally inflating multiverse using the first approach which begins with global spacetime. They showed that the multiverse exists on spatial region “R” (which has finite volume), surrounded by an inverted island ‘I’, in a bubble universe. They also suggested that, the fundamental degrees of freedom associated with certain finite spatial regions describes the semiclassical physics of multiverse, which allows them to address cosmological measure problem.
“While one might feel that this is too drastic a conclusion, in some respects it is not. What happens in the multiverse is an”inside out” version of the black hole case”
In the black hole case, the region R encloses I, so I looks geographically like an island. However, in Langhoff et al. setup (as shown in fig. 1 above), I encloses R so it no longer appears as an island. Thus, we can call I an “inverted island”.
In other words, you can treat the regions R and I as “land” and everything else as “water.” Following this convention, cauchy surface Ξ has a central land R surrounded by a moat ¯R ∪ IΞ¯ which separates R from IΞ, where IΞ = D(I)∩Ξ. To describe the multiverse at the semiclassical level, one only needs fundamental degrees of freedom associated with the complement of IΞ on Ξ, ¯IΞ¯ = R∪(¯R ∪ IΞ¯). This is the region corresponding to the castle, where the multiverse lives in.
“The island arises due to mandatory collisions with collapsing bubbles, whose big crunch singularities indicate redundancies of the global spacetime description.”
Finally, they concluded that, the emergence of the island and the resulting reduction of independent degrees of freedom provides a regularization of infinities which caused the cosmological measure problem. Their paper strongly suggests the existence of a description of the multiverse on finite spatial regions.
Reference: Kevin Langhoff, Chitraang Murdia, Yasunori Nomura, “The Multiverse in an Inverted Island”, Arxiv, pp. 1-11, 2021. https://arxiv.org/abs/2106.05271
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○ Alexander Shatskiy considered a technique of calculating deflection of the light passing through wormholes (from one universe to another). He found fundamental and characteristic features of electromagnetic radiation passing through the wormholes.
○ He showed that the distortion of the light rays that had passed through the WH throat is caused not only by redistributing of the star density, but also by changes in their apparent brightness.
○ He also implied that if angular resolution of the observer’s instrument in our Universe is high enough, he will be able to discover the changing star density in the throat J(h).
○ He also showed that the apparent brightness of the WH’s part inside its throat does not depend on impact parameter.
Alexander Shatskiy considered a technique of calculating deflection of the light passing through wormholes (from one universe to another). He found fundamental and characteristic features of electromagnetic radiation passing through the wormholes. Making use of this, he proposed new methods of observing distinctive differences between wormholes and other objects as well as methods of determining characteristic parameters for different wormhole models.
By modifying Einstein equations, he first obtained the explicit analytical form of the solution to the first order in the small correction δ ( being defined by the equation-of-state of the matter in the WH) and then transcendental equation yielding the throat radius.
In order to know, what causes the distortion of light in wormhole, he considered that the other universe contain N stars with equal luminosities and supposed N >>> 1.
Then he assumed that, all the stars are homogeneously distributed over the celestial sphere in the other universe. An observer in our Universe who is looking at the stars in the other universe through the WH throat sees them inhomogeneously distributed over the throat. This is because of the fact that the WH throat refracts and distorts the light of these stars. The distortion will obviously be spherically symmetric with the throat center being the symmetry center.
Later, he assumed that the observer look only at the fraction of the stars seen in the thin ring with the center coinciding with the throat center, the ring radius being h and its width – dh. Hence, the observer surveys the solid angle dΩ of the other universe and, moreover, dΩ = 2π|sin θ| dθ. Here, θ(h) is the deflection angle of light rays passing through the WH throat measured relative to the rectilinear propagation (By convention, the rectilinear propagation means the trajectory passing through the center of the WH throat) . Since the total solid angle equals 4π, the observer can see dN = N dΩ/(4π) stars in the ring (Since the light deflection angle θ can exceed π, the total solid angle turns out to be more than 4π. This change, however, reduces to another constant (instead of 4π) and does not affect the final result.). Furthermore, the apparent density of the stars (per unit area of the ring dS = 2πh dh) is J = dN/dS. He, therefore, obtain:
Equation 1
The dependance θ(h),
Equation 2
where, the notations η ≡ 1/x and h˜ ≡ h/q were used. This yields
Equation 3
Taking advantage of all these formulae, they found the expression for the apparent density of the stars J(h) in the wormhole.
He noted that, 2nd formula/equation also gives the maximum possible impact parameter h = hmax which still allows the observer to see the stars of the other universe. This parameter corresponds to a zero of the second factor in the radicand in (2). Namely, hmax is equal to the least possible value of the function e^–φ / η. Having conducted trivial inquiry, he obtained:
as δ → 0.
What all these equations actually showed that the distortion of the light rays that had passed through the WH throat is caused not only by redistributing of the star density, but also by changes in their apparent brightness. Namely, as the impact parameter h increases the stellar brightness changes. This is because of the fact that as the radius h of the ring, through which the star light passes, increases, an element of the solid angle where this light scatters changes as well. The respective change in the stellar brightness is proportional to the quantity κ = dS/dΩ. Therefore, the total brightness of all the stars seen on unit area of the above-mentioned ring is dN · κ/dS.
Thus, he obtained that as N → ∞ the apparent brightness of the WH’s part inside its throat does not depend on impact parameter and, regardless of which WH model he used, the WH looks like a homogeneous spot in every wavelength range.
In spite the result obtained stating that the light distribution in the WH throat is homogeneous for each WH model, he also noted that in the real universe the number of visible stars is finite, though big. This implies that if angular resolution of the observer’s instrument in our Universe is high enough, he will be able to discover the changing star density in the throat J(h).
The left panel of Fig. 1 shows this plot for δ = 0.001. Sharp minima on the plot correspond to zeros of the sine in equation 1. This is because at sufficiently large impact parameters the light rays are deflected by large angles (θ > π) so that in the vicinities of the points θ = πn abrupt declines in distribution arise. But near these declines the observed stellar brightness tends to infinity (lensing), which ultimately provides the (on average) uniform light flow over the WH throat (see the right panel of Fig. 1).
Positions of the declines depend on the value of δ. Hence, registering them makes it possible to determine the equation-of-state parameters of the WH matter and features of the WH model (which is highly analogous to processing the light spectra).
Reference: Alexander Shatskiy, “Image of another universe being observed through a wormhole throat”, Astronomical Journal, pp. 1-6, 2012. https://arxiv.org/abs/0809.0362
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The Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) is home to many interdisciplinary projects which benefit from the synergy of a wide range of expertise available at the institute. One such project is the study of black holes that could have formed in the early universe, before stars and galaxies were born.
Fig 1. Baby universes branching off of our universe shortly after the Big Bang appear to us as black holes. (Credit：Kavli IPMU)
Such primordial black holes (PBHs) could account for all or part of dark matter, be responsible for some of the observed gravitational waves signals, and seed supermassive black holes found in the center of our Galaxy and other galaxies. They could also play a role in the synthesis of heavy elements when they collide with neutron stars and destroy them, releasing neutron-rich material. In particular, there is an exciting possibility that the mysterious dark matter, which accounts for most of the matter in the universe, is composed of primordial black holes. The 2020 Nobel Prize in physics was awarded to a theorist, Roger Penrose, and two astronomers, Reinhard Genzel and Andrea Ghez, for their discoveries that confirmed the existence of black holes. Since black holes are known to exist in nature, they make a very appealing candidate for dark matter.
The recent progress in fundamental theory, astrophysics, and astronomical observations in search of PBHs has been made by an international team of particle physicists, cosmologists and astronomers, including Kavli IPMU members Alexander Kusenko, Misao Sasaki, Sunao Sugiyama, Masahiro Takada and Volodymyr Takhistov.
Fig 2. Hyper Suprime-Cam (HSC) is a gigantic digital camera on the Subaru Telescope (Credit：HSC project / NAOJ)
To learn more about primordial black holes, the research team looked at the early universe for clues. The early universe was so dense that any positive density fluctuation of more than 50 percent would create a black hole. However, cosmological perturbations that seeded galaxies are known to be much smaller. Nevertheless, a number of processes in the early universe could have created the right conditions for the black holes to form.
One exciting possibility is that primordial black holes could form from the “baby universes” created during inflation, a period of rapid expansion that is believed to be responsible for seeding the structures we observe today, such as galaxies and clusters of galaxies. During inflation, baby universes can branch off of our universe. A small baby (or “daughter”) universe would eventually collapse, but the large amount of energy released in the small volume causes a black hole to form.
An even more peculiar fate awaits a bigger baby universe. If it is bigger than some critical size, Einstein’s theory of gravity allows the baby universe to exist in a state that appears different to an observer on the inside and the outside. An internal observer sees it as an expanding universe, while an outside observer (such as us) sees it as a black hole. In either case, the big and the small baby universes are seen by us as primordial black holes, which conceal the underlying structure of multiple universes behind their “event horizons.” The event horizon is a boundary below which everything, even light, is trapped and cannot escape the black hole.
Fig 3. The Subaru Telescope in Hawaii. (Credit：NAOJ)Fig 4. A star in the Andromeda galaxy temporarily becomes brighter if a primordial black hole passes in front of the star, focusing its light in accordance with the theory of gravity. (Credit: Kavli IPMU/HSC Collaboration)
In their paper, the team described a novel scenario for PBH formation and showed that the black holes from the “multiverse” scenario can be found using the Hyper Suprime-Cam (HSC) of the 8.2m Subaru Telescope, a gigantic digital camera — the management of which Kavli IPMU has played a crucial role — near the 4,200 meter summit of Mt. Mauna Kea in Hawaii. Their work is an exciting extension of the HSC search of PBH that Masahiro Takada, a Principal Investigator at the Kavli IPMU, and his team are pursuing. The HSC team has recently reported leading constraints on the existence of PBHs in Niikura, Takada et. al. (Nature Astronomy 3, 524-534 (2019))
Why was the HSC indispensable in this research? The HSC has a unique capability to image the entire Andromeda galaxy every few minutes. If a black hole passes through the line of sight to one of the stars, the black hole’s gravity bends the light rays and makes the star appear brighter than before for a short period of time. The duration of the star’s brightening tells the astronomers the mass of the black hole. With HSC observations, one can simultaneously observe one hundred million stars, casting a wide net for primordial black holes that may be crossing one of the lines of sight.
The first HSC observations have already reported a very intriguing candidate event consistent with a PBH from the “multiverse,” with a black hole mass comparable to the mass of the Moon. Encouraged by this first sign, and guided by the new theoretical understanding, the team is conducting a new round of observations to extend the search and to provide a definitive test of whether PBHs from the multiverse scenario can account for all dark matter.
References: Alexander Kusenko, Misao Sasaki, Sunao Sugiyama, Masahiro Takada, Volodymyr Takhistov, Edoardo Vitagliano. Exploring Primordial Black Holes from the Multiverse with Optical Telescopes. Physical Review Letters, 2020; 125 (18) DOI: 10.1103/PhysRevLett.125.181304 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.181304
According to authors, if we place two massive objects in two parallel universes (modeled by two branes). Gravitational attraction between the objects competes with the resistance coming from the brane tension. For sufficiently strong attraction, the branes are deformed, objects touch and a wormhole is formed.
“Our analysis indicated that more massive and compact objects are more likely to fulfill the conditions for wormhole formation. This implies that we should be looking for wormholes either in the background of black holes and compact stars, or massive microscopic relics.”, said Skojkovic.
To get some feeling for the orders of magnitude, they calculated that two solar mass objects can form a wormhole like structure for reasonable values of brane tension and distance between the branes.
Strictly speaking, what they discuss in their paper are, wormhole-like structures rather than wormholes in strict sense. They make this distinction because they deal with some global properties of the space-time rather than local geometry. The precise metric of the wormhole-like structure would depend on the concrete massive objects researchers are talking about. If objects located in two parallel universes exerting gravitational force on each other are black holes, then the resulting wormhole would not be traversable due to the presence of the horizon. If the objects in question are neutron stars of other horizon-less objects, then the wormhole would be traversable.
They also note that the role of negative energy density which provides repulsion that counteracts gravity is played by the brane tension. Thus they do not need extra source of negative energy density in their setup to support gravity. However, this still does not guarantee stability of the whole construct. It could happen that a very long wormhole throat breaks into smaller pieces in order to minimize its energy. To verify this, a full stability analysis would be required. They leave this question for further investigation.
“There is a huge range in parameter space that allows for wormhole creation in our setup. Since the balance between the brane tension and mass (and size) of the objects is required, from Equation
we see that if the brane tension is zero, any non-zero mass would be sufficient to form a wormhole. Similarly, if the brane tension is infinite, one would need an infinitely massive object to form a wormhole. Thus, apriory there is no minimal nor maximal max required to form a wormhole.”, said Djordje Minic.
However, from the plot in Fig. given below they saw that for a fixed brane tension and fixed mass more compact objects are more likely to form wormholes.
They concluded that, “related issues reserved for future investigation that could possibly be answered in the same or similar framework including the question whether wormholes are produced before or after (brane of bulk) inflation, and whether they are stable on cosmological timescales.
References: De-Chang Dai, Djordje Minic, Dejan Stojkovic, “How to form a wormhole”, ArXiv, pp. 1-6, 2020. https://arxiv.org/abs/2010.03947v2
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