Baby Universes Research Articles

Multi-critical behaviour of 4-dimensional tensor models up to order 6

Tensor models generalize the matrix-model approach to 2-dimensional quantum gravity to higher dimensions. Some models allowing a 1/N expansion have been explored, most of them generating branched-polymer geometries. Recently, enhancements yielding an additional 2d pure gravity (planar) phase and an intermediate regime of proliferating baby universes have been found. It remains an open issue to find models escaping these lower-dimensionality universality classes.Here we analyse the dominant regime and critical behaviour of a range of new models which are candidates for such effective geometries, in particular interactions based on the utility graph K3,3. We find that, upon proper enhancement, the two-phase structure of a branched-polymer and a 2d gravity regime is the common case in U(N)-invariant rank D=4 tensor models of small orders. Not only the well known so-called necklace interactions but also K3,3-type interactions turn out as the source for the planar regime. We give a systematic account of the enhancement scaling, the counting of leading-order diagrams and the multi-critical behaviour of a wide range of interactions, in particular for all order-6 interactions of rank 3 and 4. These findings support the claim of universality of such mixtures of branched-polymer and planar diagrams at criticality. In particular, this hints at the necessity to consider new ingredients, or interactions of higher order and rank, in order to obtain higher dimensional continuum geometry from tensor models.

Euclidean Wormholes, Baby Universes, and Their Impact on Particle Physics and Cosmology

The euclidean path integral remains, in spite of its familiar problems, an important approach to quantum gravity. One of its most striking and obscure features is the appearance of gravitational instantons or wormholes. These renormalize all terms in the Lagrangian and cause a number of puzzles or even deep inconsistencies, related to the possibility of nucleation of "baby universes". In this review, we revisit the early controversies surrounding these issues as well as some of the more recent discussions of the phenomenological relevance of gravitational instantons. In particular, wormholes are expected to break the shift symmetries of axions or Goldstone bosons non-perturbatively. This can be relevant to large-field inflation and connects to arguments made on the basis of the Weak Gravity or Swampland conjectures. It can also affect Goldstone bosons which are of physical interest in the context of the strong CP problem or as dark matter.

The Third Quantization: To Tunnel or Not to Tunnel?

Within the framework of the third quantization, we consider the possibility that an initially recollapsing baby universe can enter a stage of near de Sitter inflation by tunnelling through a Euclidean wormhole that connects the recollapsing and inflationary geometries. We present the solutions for the evolution of the scale factor in the Lorentzian and Euclidean regions as well as the probability that the baby universe indeed crosses the wormhole when it reaches its maximum size.

A modified Friedmann equation

We recently formulated a model of the universe based on an underlying W3-symmetry. It allows the creation of the universe from nothing and the creation of baby universes and wormholes for spacetimes of dimension 2, 3, 4, 6 and 10. Here we show that the classical large time and large space limit of these universes is one of exponential fast expansion without the need of a cosmological constant. Under a number of simplifying assumptions, our model predicts that w = −1.2 in the case of four-dimensional spacetime. The possibility of obtaining a w-value less than −1 is linked to the ability of our model to create baby universes and wormholes.

Primordial black hole formation by vacuum bubbles

Vacuum bubbles may nucleate during the inflationary epoch and expand, reaching relativistic speeds. After inflation ends, the bubbles are quickly slowed down, transferring their momentum to a shock wave that propagates outwards in the radiation background. The ultimate fate of the bubble depends on its size. Bubbles smaller than certain critical size collapse to ordinary black holes, while in the supercritical case the bubble interior inflates, forming a baby universe, which is connected to the exterior region by a wormhole. The wormhole then closes up, turning into two black holes at its two mouths. We use numerical simulations to find the masses of black holes formed in this scenario, both in subcritical and supercritical regime. The resulting mass spectrum is extremely broad, ranging over many orders of magnitude. For some parameter values, these black holes can serve as seeds for supermassive black holes and may account for LIGO observations.

What if? Exploring the multiverse through Euclidean wormholes

We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era.

Sloshing, supersonic gas may have built the baby universe’s biggest black holes

Sloshing, supersonic gas may have built the baby universe’s biggest black holes

The Brownian plane with minimal neck baby universe

AbstractFor each , let be a uniform rooted quadrangulation, endowed with an appropriate measure, of size n conditioned to have r(n) vertices in its root block. We prove that for a suitable function r(n), after rescaling graph distance by converges to a random pointed non‐compact metric measure space , in the local Gromov‐Hausdorff‐Prokhorov topology. The space is built by identifying a uniform point of the Brownian map with the distinguished point of the Brownian plane. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 729–752, 2017

Primordial black hole and wormhole formation by domain walls

In theories with a broken discrete symmetry, Hubble sized spherical domain walls may spontaneously nucleate during inflation. These objects are subsequently stretched by the inflationary expansion, resulting in a broad distribution of sizes. The fate of the walls after inflation depends on their radius. Walls smaller than a critical radius fall within the cosmological horizon early on and collapse due to their own tension, forming ordinary black holes. But if a wall is large enough, its repulsive gravitational field becomes dominant much before the wall can fall within the cosmological horizon. In this ``supercritical'' case, a wormhole throat develops, connecting the ambient exterior FRW universe with an interior baby universe, where the exponential growth of the wall radius takes place. The wormhole pinches off in a time-scale comparable to its light-crossing time, and black holes are formed at its two mouths. As discussed in previous work, the resulting black hole population has a wide distribution of masses and can have significant astrophysical effects. The mechanism of black hole formation has been previously studied for a dust-dominated universe. Here we investigate the case of a radiation-dominated universe, which is more relevant cosmologically, by using numerical simulations in order to find the initial mass of a black hole as a function of the wall size at the end of inflation. For large supercritical domain walls, this mass nearly saturates the upper bound according to which the black hole cannot be larger than the cosmological horizon. We also find that the subsequent accretion of radiation satisfies a scaling relation, resulting in a mass increase by about a factor of 2.

Classical conformality in the Standard Model from Coleman’s theory

The classical conformality (CC) is one of the possible candidates for explaining the gauge hierarchy of the Standard Model (SM). We show that it is naturally obtained from the Coleman’s theory on baby universe.

Quantum self-gravitating collapsing matter in a quantum geometry

The problem of how space–time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole.

Large N Limits in Tensor Models: Towards More Universality Classes of Colored Triangulations in Dimension d≥2

We review an approach which aims at studying discrete (pseudo-)manifolds in dimension $d\geq 2$ and called random tensor models. More specifically, we insist on generalizing the two-dimensional notion of $p$-angulations to higher dimensions. To do so, we consider families of triangulations built out of simplices with colored faces. Those simplices can be glued to form new building blocks, called bubbles which are pseudo-manifolds with boundaries. Bubbles can in turn be glued together to form triangulations. The main challenge is to classify the triangulations built from a given set of bubbles with respect to their numbers of bubbles and simplices of codimension two. While the colored triangulations which maximize the number of simplices of codimension two at fixed number of simplices are series-parallel objects called melonic triangulations, this is not always true anymore when restricting attention to colored triangulations built from specific bubbles. This opens up the possibility of new universality classes of colored triangulations. We present three existing strategies to find those universality classes. The first two strategies consist in building new bubbles from old ones for which the problem can be solved. The third strategy is a bijection between those colored triangulations and stuffed, edge-colored maps, which are some sort of hypermaps whose hyperedges are replaced with edge-colored maps. We then show that the present approach can lead to enumeration results and identification of universality classes, by working out the example of quartic tensor models. They feature a tree-like phase, a planar phase similar to two-dimensional quantum gravity and a phase transition between them which is interpreted as a proliferation of baby universes.

Black holes and the multiverse

Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive black holes. The mechanism of black hole formation described in this paper is very generic and has important implications for the global structure of the universe. Baby universes inside super-critical black holes inflate eternally and nucleate bubbles of all vacua allowed by the underlying particle physics. The resulting multiverse has a very non-trivial spacetime structure, with a multitude of eternally inflating regions connected by wormholes. If a black hole population with the predicted mass spectrum is discovered, it could be regarded as evidence for inflation and for the existence of a multiverse.

Using a Multiverse Version of Penrose Cyclic Conformal Cosmology to Obtain Ergodic Mixing Averaging of Cosmological Information Transfer to Fix H Bar (Planck’s Constant) in Each New Universe Created during Recycling of Universes Due to CCC, Multiverse Style

What we are doing is to use a generalization of the Penrose Cyclic conformal cosmology in order to argue for ergodic mixing of cosmological “information”, from cycle to cycle. While there would be a causal discontinuity, as is by example explained, in terms of breaking down of individual “particles” from cycle to cycle, there would be (analogous to a seed setting of pseudo-randomization of Fortran) informational “bits” transferred, as far as mixing of “information” collected from cycle to cycle, from N number of contributing universes via modified CCC, so as to create a uniform value of H bar (Planck’s constant) from cycle to cycle. Moreover this would do away with the “baby universes” Darwinian hypothesis, set up by String theorists whom postulate that up to 101000 or so universes would be created, with only say 1010 or so surviving (most dying off) because of “improperly” set variance in the values of H bar (Planck’s constant). i.e. the laws of physics would not be different from universe to universe.

Separate universe problem: 40 years on

The claim that an overdense (positive curvature) region in the early universe cannot extend beyond some maximum scale and remain part of our universe, first made 40 years ago, has recently been questioned by Kopp et al. Their analysis is elucidating and demonstrates that one cannot constrain the form of primordial density perturbations using this argument. However, the notion of a separate-universe scale still applies and it places an important upper limit on the mass of primordial black holes forming at any epoch. We calculate this scale for equations of state of the form $p = k \rho c^2$ with $-1 <k < \infty$, refining earlier calculations on account of the Kopp et al. criticisms. For $-1/3 < k < \infty$, the scale is always of order the cosmological particle horizon size, with a numerical factor depending on $k$. This confirms the earlier claim that a primordial black hole cannot be much larger than the particle horizon at formation. For $-1 < k< -1/3$, as expected for some periods in the history of the universe, the situation changes radically, in that a sufficiently large positive-curvature region produces a baby universe rather than a black hole. There is still a separate-universe scale but the interpretation of these solutions requires care.

Torsional instanton effects in quantum gravity

We show that, in the first order gravity theory coupled to axions, the instanton number of the Giddings-Strominger wormhole can be interpreted as the Nieh-Yan topological index. The axion charge of the baby universes is quantized in terms of the Nieh-Yan integers. Tunneling between universes of different Nieh-Yan charges implies a nonperturbative vacuum state. The associated topological vacuum angle can be identified with the Barbero-Immirzi parameter.

Remnants, fuzzballs or wormholes?

The black hole information paradox has caused enormous confusion over four decades. But in recent years, the theorem of quantum strong-subadditivity has sorted out the possible resolutions into three sharp categories: (i) No new physics at r ≫ lp; this necessarily implies remnants/information loss. A realization of remnants is given by a baby universe attached near r ~ 0. (ii) Violation of the "no-hair" theorem by nontrivial effects at the horizon r ~ M. This possibility is realized by fuzzballs in string theory, and gives unitary evaporation. (iii) Having the vacuum at the horizon, but requiring that Hawking quanta at r ~ M3 be somehow identified with degrees of freedom inside the black hole. A model for this "extreme nonlocality" is realized by conjecturing that wormholes connect the radiation quanta to the hole.

New Neutrino May Have Heated Baby Universe

A new analysis of the way galaxies are distributed through space suggests that some of the universe's dark matter may consist of hitherto undiscovered particles known as sterile neutrinos.

The generalized second law implies a quantum singularity theorem

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose’s original singularity theorem, it implies that spacetime is null-geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann–Robertson–Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. The introduction describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.)

The quantum entanglement between colorful dark energy universes in a colorful multiverse

Recently, a model for colorful black hole production and decay in proton–proton collisions has been constructed. These results can be extended to a multiverse, because it is obvious that there is enough energy in cosmic rays to produce a baby Universe. It is observed that these Universes are defined by their gauge charges. Notably, Universes can have a color charge. This is not in contradiction with confinement because the typical length scale of QCD (i.e., a Fermi) is much larger than the size of a baby Universe at its birth. These colorful Universes can interact with each other, annihilate, and form a color singlet Universe. Next, it is argued that color confinement may generate an entanglement between colorful dark energy Universes to form a color singlet binary system. Finally, the production cross section for entangled colorful dark energy Universes in a multiverse is obtained. It is found that the cross section of a Friedmann–Robertson–Walker Universe is much larger for smaller values of the Hubble parameter. Also, this cross section is greater for entangled open Universes and smaller for entangled closed Universes.