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Alexander Vilenkin

Publications and source records attributed to Alexander Vilenkin.

At least 19 recordsLinked to original sources
arXiv2025

On quantum creation of a toroidal universe

We consider the quantum creation of a universe with flat spatial sections and the topology of a 3-torus, taking into account the effect of Casimir energy. We show that the corresponding instantons are singular. Since these instantons describe universes originating in a state of infinite energy, we argue that they cannot be interpreted as quantum creation from `nothing'. If quantum corrections to the energy-momentum tensor are neglected, the spacetime of the toroidal universe reduces to de Sitter space with appropriate periodic identifications. Contrary to previous claims in the literature, this spacetime is geodesically incomplete. We argue that this spacetime describes a classical universe originating at a singularity, and not a quantum origin. 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. We therefore see no reasonable way to compare the probability of creation of a toroidal universe, if it is possible at all, with that of a spherical universe.

gr-qc↗
arXiv2024

Global String Instantons

We study the formation of gravitating global strings through quantum mechanical tunneling. The instantons that describe the nucleation process are characterized by two parameters: the string core thickness and its gravitational backreaction controlled by the string core energy density. We obtain solutions across a wide range of these parameters by carrying out numerical integration via multiple shooting methods. Our results are in agreement with previous findings on the nucleation of other topological defects; specifically, after reaching a certain threshold for the string core thickness or its gravitational backreaction, the configuration becomes homogeneous in a manner akin to Hawking-Moss solutions. Additionally, we analyze the global structure of the analytical continuation of the solutions to Lorentzian signature, revealing the emergence of a region of spacetime that describes an anisotropic universe. Finally, we also discuss the relevance of these instantons in the context of quantum cosmology.

gr-qc↗
arXiv2023

What determines the rest frame of bubble nucleation?

We revisit the question addressed in recent papers by Garriga et al: What determines the rest frame of pair nucleation in a constant electric field? The conclusion reached in these papers is that pairs are observed to nucleate at rest in the rest frame of the detector which is used to detect the pairs. A similar conclusion should apply to bubble nucleation in a false vacuum. This conclusion however is subject to doubt due to the unphysical nature of the model of a constant eternal electric field that was used by Garriga et al. The number density of pairs in such a field would be infinite at any finite time. Here we address the same question in a more realistic model where the electric field is turned on at a finite time $t_0$ in the past. The process of turning on the field breaks the Lorentz invariance of the model and could in principle influence the frame of pair nucleation. We find however that the conclusion of Garriga et al still holds in the limit $t_0 \to -\infty$. This shows that the setup process of the electric field does not have a lasting effect on the observed rest frame of pair nucleation. {On the other hand, the electric current and charge density due to the pairs are determined by the way in which the electric field was turned on.

hep-th↗
arXiv2023

Simulating cosmic string loop captured by a rotating black hole

We study the dynamics of a cosmic string loop captured by a rotating black hole, ignoring string reconnections. A loop is numerically evolved in Kerr spacetime, with the result that it turns into one or more growing or contracting double-lines rotating around the black hole in the equatorial plane. This is in good agreement with the approximate analytical treatment of the problem investigated by Xing et al., who studied the evolution of the auxiliary curve associated with the string loop. We confirm that the auxiliary curve deformation can indeed describe the string motion in realistic physical scenarios to a reasonable accuracy, and can thus be used to further study other phenomena such as superradiance and reconnections of the captured loop.

gr-qc↗
arXiv2023

Quantum cosmology, eternal inflation, and swampland conjectures

In light of the recent swampland conjectures, we explore quantum cosmology and eternal inflation beyond the slow roll regime. We consider a model of a closed universe with a scalar field $ϕ$ in the framework of tunneling approach to quantum cosmology. The scalar field potential is assumed to have a maximum at $ϕ=0$ and can be approximated in its vicinity as $V(ϕ)\approx 3H^{2}-\frac{1}{2}m^{2}ϕ^{2}$. Using the instanton method, we find that for $m<2H$ the dominant nucleation channel for the universe is tunneling to a homogeneous, spherical de Sitter space. For larger values of $m/H$, the most probable tunneling is to an inhomogeneous closed universe with a domain wall wrapped around its equator. We determine the quantum state of the field $ϕ$ in the nucleated universe by solving the Wheeler-DeWitt equation with tunneling boundary conditions. Our results agree with earlier work which assumed a slow-roll regime $m\ll H$. We finally show that spherical universes nucleating with $m<2H$ undergo stochastic eternal inflation with inflating regions forming a fractal of dimension $d>2$. For larger values of $m$ the field $ϕ$ is unstable with respect to formation of domain walls and cannot be described by a perturbative stochastic approach.

gr-qc↗
arXiv2022

The tunneling wavefunction in Kantowski-Sachs quantum cosmology

We use a path-integral approach to study the tunneling wave function in quantum cosmology with spatial topology $S^{1}\times S^{2}$ and positive cosmological constant (the Kantowski-Sachs model). If the initial scale factors of both $S^1$ and $S^2$ are set equal to zero, the wave function describes (semiclassically) a universe originating at a singularity. This may be interpreted as indicating that an $S^1\times S^2$ universe cannot nucleate out of nothing in a non-singular way. Here we explore an alternative suggestion by Halliwell and Louko that creation from nothing corresponds in this model to setting the initial volume to zero. We find that the only acceptable version of this proposal is to fix the radius of $S^1$ to zero, supplementing this with the condition of smooth closure (absence of a conical singularity). The resulting wave function predicts an inflating universe of high anisotropy, which however becomes locally isotropic at late times. Unlike the de Sitter model, the total nucleation probability is not exponentially suppressed, unless a Gauss-Bonnet term is added to the action.

gr-qc↗
arXiv2021

Jackiw-Teitelboim and Kantowski-Sachs quantum cosmology

We study quantum cosmology of the $2D$ Jackiw-Teitelboim (JT) gravity with $Λ>0$ and calculate the Hartle-Hawking (HH) wave function for this model in the minisuperspace framework. Our approach is guided by the observation that the JT dynamics can be mapped exactly onto that of the Kantowski-Sachs (KS) model describing a homogeneous universe with spatial sections of $S^1\times S^2$ topology. This allows us to establish a JT-KS correspondence between the wave functions of the models. We obtain the semiclassical Hartle-Hawking wave function by evaluating the path integral with appropriate boundary conditions and employing the methods of Picard-Lefschetz theory. The JT-KS connection formulas allow us to translate this result to JT gravity, define the HH wave function and obtain a probability distribution for the dilaton field.

gr-qc↗
arXiv2021

Black holes and up-tunneling suppress Boltzmann brains

Eternally inflating universes lead to an infinite number of Boltzmann brains but also an infinite number of ordinary observers. If we use the scale factor measure to regularize these infinities, the ordinary observers dominate the Boltzmann brains if the vacuum decay rate of each vacuum is larger than its Boltzmann brain nucleation rate. Here we point out that nucleation of small black holes should be counted in the vacuum decay rate, and this rate is always larger than the Boltzmann brain rate, if the minimum Boltzmann brain mass is more than the Planck mass. We also discuss nucleation of small, rapidly inflating regions, which may also have a higher rate than Boltzmann brains. This process also affects the distribution of the different vacua in eternal inflation.

hep-th↗
arXiv2021

No black holes from cosmic string cusps

Recent work by Jenkins and Sakellariadou claims that cusps on cosmic strings lead to black hole production. To derive this conclusion they use the hoop conjecture in the rest frame of the string loop, rather than in the rest frame of the proposed black hole. Most of the energy they include is the bulk motion of the string near the cusp. We redo the analysis taking this into account and find that cusps on cosmic strings with realistic energy scale do not produce black holes, unless the cusp parameters are extremely fine-tuned.

astro-ph.CO↗
arXiv2020

Bubble nucleation as seen by different observers

Pair production in a constant electric field is closely analogous to bubble nucleation in a false vacuum. The classical trajectories of the pairs are Lorentz invariant, but this invariance should be broken by the nucleation process. Garriga et al. used a model detector, consisting of other particles interacting with the pairs, to investigate how pair production is seen by different Lorentzian observers. They found that particles (antiparticles) of the pair are predominantly observed moving in the direction of (opposite to) the electric field and concluded that observers see pairs nucleating preferentially in the detector's rest frame. Here, we apply this approach to the case where two detectors moving relative to one another are used to observe the particle and antiparticle of the same pair. We find that each detector will still observe nucleation to occur in its rest frame, regardless of the motion of the other detector. However, if the relative velocity of the two detectors is sufficiently high, the particle and antiparticle of the pair can be observed moving towards one another with arbitrarily large momenta, contrary to the usual expectation.

hep-th↗
arXiv2020

Spinning black holes as cosmic string factories

We consider the evolution of a cosmic string loop that is captured by a much more massive and compact black hole. We show that after several reconnections that produce ejections of smaller loops, the loop that remains bound to the black hole moves on a nearly-periodic non-self-intersecting trajectory, "the orbit". The orbit evolves due to an energy and angular momentum exchange between the loop and the spinning black hole. We show that such evolution is mathematically equivalent to a certain continuous deformation of an auxiliary closed curve in a 3-dimensional space; for zero black-hole spin this deformation is curve-shortening that has been extensively studied by mathematicians. The evolution features competing effects of loop growth by the superradiant extraction of the black-hole spin energy, and loop decay by the friction of the moving string against the horizon. A self-intersection of an auxiliary curve corresponds to a capture by the black hole of a new string segment and thus an addition of a new captured loop. Possible asymptotic states of such evolution are shown to be strong emitters of gravitational waves. Whether reconnections prevent reaching the asymptotic states remains to be explored. Additionally, the orbit's shape also evolves due to an emission of gravitational waves, and a recoil of the black hole that changes the orbit and likely leads to self-intersections. We argue that for a significant range of the dimensionless tension $μ$, string loops are captured by supermassive black holes at the centers of galaxies. This strongly motivates further study of interaction between string loops and black holes, especially the influence of this process on the black hole spindown and on the production of gravitational waves by strings created in galactic nuclei. We also discuss potential loop captures by primordial black holes.

astro-ph.HE↗
arXiv2020

Clustering of cosmic string loops

Observational effects of cosmic string loops depend on how loops are distributed in space. Chernoff \cite{Chernoff} has argued that loops can be gravitationally captured in galaxies and that for sufficiently small values of $Gμ$ their distribution follows that of dark matter, independently of the loop's length. We re-analyze this issue using the spherical model of galaxy formation with full account taken of the gravitational rocket effect -- loop accelerated motion due to asymmetric emission of gravitational waves. We find that only loops greater than a certain size are captured and that the number of captured loops is orders of magnitude smaller than estimated by Chernoff.

astro-ph.CO↗
arXiv2019

4-volume cutoff measure of the multiverse

Predictions in an eternally inflating multiverse are meaningless unless we specify the probability measure. The scale-factor cutoff is perhaps the simplest and most successful measure which avoid catastrophic problems such as the youngness paradox, runaway problem, and Boltzmann brain problem, but it is not well defined in contracting regions with a negative cosmological constant. In this paper, we propose a new measure with properties similar to the scale-factor cutoff which is well defined everywhere. The measure is defined by a cutoff in the 4-volume spanned by infinitesimal comoving neighborhoods in a congruence of timelike geodesics. The probability distributions for the cosmological constant and for the curvature parameter in this measure are similar to those for the scale factor cutoff and are in a good agreement with observations.

hep-th↗
arXiv2019

Eternal Inflation in Swampy Landscapes

The much-discussed swampland conjectures suggest significant constraints on the properties of string theory landscape and on the nature of the multiverse that this landscape can support. The conjectures are especially constraining for models of inflation; in particular, they exclude the existence of de Sitter (dS) vacua. If the conjectures are false and dS vacua do exist, it still appears that their construction in string theory requires a fair amount of fine-tuning, so they may be vastly outnumbered by AdS vacua. Here we explore the multiverse structure suggested by these considerations. We consider two scenarios: (i) a landscape where dS vacua are rare and (ii) a landscape where dS vacua do not exist and the dS potential maxima and saddle points are not flat enough to allow for the usual hilltop inflation, even though slow-roll inflation is possible on the slopes of the potential. We argue that in both scenarios inflation is eternal and all parts of the landscape that can support inflation get represented in the multiverse. The spacetime structure of the multiverse in such models is nontrivial and is rather different from the standard picture.

gr-qc↗
arXiv2019

Quantum instability of an oscillating universe

An oscillating, compact Friedmann universe with a massive conformally coupled scalar field is studied in the framework of quantum cosmology. The scalar field is treated as a perturbation and we look for solutions of the Wheeler-DeWitt equation describing stable stationary states of the model. We assume that the previous sources of quantum instability that have been discussed in the literature (particle production, and tunnelling to zero size) are absent. We then show, under rather general assumptions, that a further source of quantum instability prevents the existence of stationary states with localized wave function in the direction of the scalar-field modes.

gr-qc↗
arXiv2019

Flyover vacuum decay

We use analytic estimates and numerical simulations to explore the stochastic approach to vacuum decay. According to this approach, the time derivative of a scalar field, which is in a local vacuum state, develops a large fluctuation and the field \flies over" a potential barrier to another vacuum. The probability distribution for the initial fluctuation is found quantum mechanically, while the subsequent nonlinear evolution is determined by classical dynamics. We find in a variety of cases that the rate of such flyover transitions has the same parametric form as that of tunneling transitions calculated using the instanton method, differing only by a numerical factor O(1) in the exponent. An important exception is an "upward" transition from a de Sitter vacuum to a higher-energy de Sitter vacuum state. The rate of flyover transitions in this case is parametrically different and can be many orders of magnitude higher than tunneling. This result is in conflict with the conventional picture of quantum de Sitter space as a thermal state. Our numerical simulations indicate that the dynamics of bubble nucleation in flyover transitions is rather different from the standard picture. The difference is especially strong for thin-wall bubbles in flat space, where the transition region oscillates between true and false vacuum until a true vacuum shell is formed which expands both inwards and outwards, and for upward de Sitter transitions, where the inflating new vacuum region is contained inside of a black hole.

hep-th↗
arXiv2019

Constraints on non-minimal coupling from quantum cosmology

Quantum cosmology is investigated in a de Sitter minisuperspace model with a quantized scalar field non-minimally coupled to curvature. Quantum states of the scalar field must satisfy the regularity condition, which requires that the probability of field fluctuations should not increase with their amplitude. We show that this condition imposes constraints on the allowed values of the curvature coupling parameter $ξ$. This is a surprising result, since the field dynamics depends only on the combination $m^2+ξR$, where $m$ is the field mass and $R = \mathrm{const}$ is the curvature, and does not depend on $ξ$ separately.

gr-qc↗