Alexander Vilenkin’s research while affiliated with Tufts University and other places

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Publications (304)


Global String Instantons
  • Preprint
  • File available

October 2024

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5 Reads

Jose J. Blanco-Pillado

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Alexander Vilenkin

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.

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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 → -∞. 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.


Simulating cosmic string loop captured by a rotating black hole

June 2023

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11 Reads

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6 Citations

Physical Review D

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.


Quantum cosmology, eternal inflation, and swampland conjectures

April 2023

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50 Reads

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4 Citations

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 )≈ 3 H ² - 1/2 m ² ϕ ² . Using the instanton method, we find that for m < 2 H 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 ≪ H . We finally show that spherical universes nucleating with m < 2 H 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.


What determines the rest frame of bubble nucleation?

February 2023

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8 Reads

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 t0t_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 t0t_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.


Quantum cosmology, eternal inflation, and swampland conjectures

February 2023

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22 Reads

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\phi in the framework of tunneling approach to quantum cosmology. The scalar field potential is assumed to have a maximum at ϕ=0\phi=0 and can be approximated in its vicinity as V(ϕ)3H212m2ϕ2V(\phi)\approx 3H^{2}-\frac{1}{2}m^{2}\phi^{2}. Using the instanton method, we find that for m<2Hm<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\phi 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 mHm\ll H. We finally show that spherical universes nucleating with m<2Hm<2H undergo stochastic eternal inflation with inflating regions forming a fractal of dimension d>2d>2. For larger values of m the field ϕ\phi is unstable with respect to formation of domain walls and cannot be described by a perturbative stochastic approach.


The tunneling wavefunction in Kantowski-Sachs quantum cosmology

August 2022

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9 Reads

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13 Citations

We use a path-integral approach to study the tunneling wave function in quantum cosmology with spatial topology S ¹ × 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 × 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.


The tunneling wavefunction in Kantowski-Sachs quantum cosmology

June 2022

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18 Reads

We use a path-integral approach to study the tunneling wave function in quantum cosmology with spatial topology S1×S2S^{1}\times S^{2} and positive cosmological constant (the Kantowski-Sachs model). If the initial scale factors of both S1S^1 and S2S^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 S1×S2S^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 S1S^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.



Jackiw-Teitelboim and Kantowski-Sachs quantum cosmology

March 2022

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30 Reads

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22 Citations

We study quantum cosmology of the 2 D 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 × 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.


Citations (67)


... 5 While not found in the numerical simulation of ref. [20], it is possible that there is a transitory period where a string becomes attached to the black hole and inhibits superradiance. The string would spin out string length until it detaches from the black hole and superradiance can begin again [31]. ...

Reference:

Searching for string bosenovas with gravitational wave detectors
Simulating cosmic string loop captured by a rotating black hole
  • Citing Article
  • June 2023

Physical Review D

... An example can be found in the inflationary scenario; Linde and Vilenkin [50,[69][70][71]] discussed the possibility, under certain hypotheses, of the existence of a self-reproducing inflationary universe described as a self-reproducing fractal structure. In this context, this scenario could be successfully seen as belonging to the class of what we call a "meta Everett Universe", without needing a specific initial choice of parameters, interpreted as an emerging self-semantically closed structure which reproduces itself during its evolution. ...

Quantum cosmology, eternal inflation, and swampland conjectures

... Notably, the coupling ρ r , determined in Appendix B and used below, is to be understood as an order-of-magnitude estimate. Independently of these theoretical uncertainties, in the parameter space relevant here, we find that the impact of the altered GW frequency evolution outweighs those 4 Strings may also be produced through other mechanisms (e.g., the Kibble mechanism active in the early universe [94]) and attach to the remnant BH [75,95]. This could halt the superradiance process and falsify the interpretation of a null result from a GW search as the absence of such particles. ...

Spinning black holes as cosmic string factories
  • Citing Article
  • April 2021

Physical Review D

... The Lorentzian path integral of the Kantowski-Sachs model has been analyzed in Refs. [49][50][51][52]. 4 In particular, the authors of Refs. [50,51] performed this analysis under the Euclidean boundary condition following the original version of the no-boundary proposal and tunneling proposal. ...

The tunneling wavefunction in Kantowski-Sachs quantum cosmology

... This model has been studied by many authors, including [14,[27][28][29][30]. In particular, [29] noticed that in the ƛ → ∞ limit, solutions (39) of the Einstein equation, which we will discuss below, develop a long ð"nearly" dS 2 Þ × S 2 throat. ...

Jackiw-Teitelboim and Kantowski-Sachs quantum cosmology

... Other approaches appeal to quantum cosmology [43][44][45][46][47][48] or count measurements along the worldline of a single observer moving through the multiverse [44,47,49,50]. More recent work on the measure problem includes [31,32,[51][52][53][54][55][56][57][58][59][60][61][62][63]. ...

Black holes and uptunneling suppress Boltzmann brains
  • Citing Article
  • July 2021

Physical Review D

... The largest velocity found, in units of c, is 0.296, and 64% of loops experience a maximum recoil velocity of greater than 10 −3 . As a result, self-intersections are a potential mechanism for unbinding loops from galaxies, where they might otherwise cluster by gravitational interactions [41,42]. This has implications for studies of the rocket effect [43,44], gravitational lensing by strings, and the detectability of bursts from strings [41,45,46]. ...

Clustering of cosmic string loops

... In our present work, we will be agnostic concerning the abundance and longevity of dS vacua. In other words, we will allow both for 'swampy' landscapes (using the terminology of [32]) in which dS is either extremely rare or non-existent, and 'rocky' landscapes with abundant dS vacua. ...

Eternal inflation in swampy landscapes