REVIEW
Recycling universe
Astrophysics · Submitted 26 Jul 1997 · 52 references
Pith's verdict: A careful, honestly-hedged extension of stochastic inflation to a recycling universe; the physics rests on an upward tunneling rate the authors themselves call suspicious, and they say so in the text.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
If the vacuum we live in still holds energy, patches of it can tunnel back into the inflating state, so the universe may cycle endlessly between inflation and a hot big bang rather than winding down.
The reading
What carries the argument
The load-bearing object is the master equation obtained by adding upward-tunneling terms to the stochastic-inflation Fokker-Planck equation: $partial_t P = -partial_varphi J - tilde{kappa}_f(varphi) P + kappa_f(varphi) p_f$, together with rate equations for the true vacua and the false vacuum, with transition rates $kappa_f = Gamma_f^{(0)} 4pi H_f^{-alpha-3}/3$ and $kappa_t = Gamma_t^{(0)} 4pi H_t^{-alpha-3}/3$. The stationary distribution follows from $M P_0 = 0$, with the ratio $p_f/p_t = (H_f/H_t)^{alpha} (Gamma_t^{(0)}/Gamma_f^{(0)})$, and the paper argues that only the Ito factor ordering ($beta = 1$) makes the time-parametrization dependence reduce to the trivial factor $H^{alpha}$. Supporting this machinery is the thin-wall bubble geometry: a false-vacuum bubble's radius grows monotonically from $H_t^{-1}$, so 'nucleation time' has to be defined by convention, and the paper shows that the product of rate and affected volume is convention-independent.
Extended reading notes
Core claim
The paper's claim is that a positive cosmological constant in the true vacuum makes inflation reversible. Because the nucleation rate for a false-vacuum bubble inside the true vacuum goes as $A e^{-S_b + S_t}$ with $S_t = -3/8rho_t$, it is non-zero whenever $rho_t > 0$, and the Lee-Weinberg conjecture says the prefactor matches the ordinary decay rate. Each such bubble seeds a new eternally inflating domain whose interior reproduces the whole sequence — slow roll, thermalization, matter and radiation domination, true-vacuum domination — and each of those domains in turn produces new false-vacuum seeds. The authors work out the geometry of these bubbles by matching two de Sitter 4-spheres of radii $H_f^{-1}$ and $H_t^{-1}$ across a thin wall, then generalize stochastic inflation to a coupled system for the false vacuum, the true vacua, and the slow-roll distribution $P(varphi,t)$. The resulting master equation $M P_0 = 0$ has a unique non-negative stationary solution, so the co-moving fractions of the phases stop drifting and settle down; the inflating region then occupies a non-vanishing fraction of the volume, giving overall fractal dimension $d=3$ rather than $d<3$, while each connected vacuum region remains a fractal of dimension below three.
Load-bearing premise
That a region of the thermalized vacuum really does tunnel back up to the inflating false vacuum at the non-zero rate the Euclidean instanton prescribes, a rate the authors themselves call 'somewhat suspicious' and say has never been derived from first principles in de Sitter space.
Editorial extensions
If this is right
- Co-moving volume in the inflating phase is continually replenished, so the inflating fraction of the universe does not vanish at late times and the global fractal dimension is $d=3$ rather than the $d<3$ of standard eternal inflation.
- The Borde-Vilenkin no-beginning theorems lose their premises: the null convergence condition is violated by fluctuations that raise the expansion rate, and the finite past-volume difference condition does not apply once inflating regions can sit to the future of a nucleation surface.
- In a model with several minima of the inflaton potential, an eternal observer visits each minimum with a frequency set by the shape of the potential, giving a stationary probability distribution over the possible sets of low-energy constants.
- The standard gauge-invariant cutoff procedure for making predictions cannot be implemented as it stands, because each co-moving region passes through an endless succession of different thermalization types rather than one.
Reading between the lines
- If the upward rate is genuinely non-zero, the natural next question is whether the stationary distribution is normalizable once a Planck-energy boundary or a zero/negative-energy minimum is included; the paper notes that loss of observers through such boundaries restores $gamma_0 > 0$ and drives the dimension below three, which suggests a sharp threshold between complete and partial recycling.
- The frequency with which an observer visits each vacuum minimum is a concrete, in-principle calculable quantity in this formalism, so a model with two or three well-separated minima could be turned into a definite numerical prediction for the ratios $p_1/p_2$ and compared across time parametrizations.
- The claim that no continuous limit connects the recycling and non-recycling regimes as tunneling probabilities go to zero is a structural statement worth checking independently: it implies the stationary distribution is a singular perturbation of the standard exponentially decaying solution, which is the kind of thing that can be tested on a stripped-down two-state toy model.
- The whole construction rests on a rate computed by continuing a Euclidean instanton, and the authors say plainly that this continuation has never been justified from first principles in de Sitter space; an independent Lorentzian or real-time derivation of false-vacuum bubble nucleation would settle the question one way or the other.
Original abstract
If the effective cosmological constant is non-zero, our observable universe may enter a stage of exponential expansion. In such case, regions of it may tunnel back to the false vacuum of an inflaton scalar field, and inflation with a high expansion rate may resume in those regions. An ``ideal'' eternal observer would then witness an infinite succession of cycles from false vacuum to true, and back. Within each cycle, the entire history of a hot universe would be replayed. If there were several minima of the inflaton potential, our ideal observer would visit each one of these minima with a frequency which depends on the shape of the potential. We generalize the formalism of stochastic inflation to analyze the global structure of the universe when this `recycling' process is taken into account.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
If the effective cosmological constant is non-zero, our observable universe may enter a stage of exponential expansion. In such case, regions of it may tunnel back to the false vacuum of an inflaton scalar field, and inflation with a high expansion rate may resume in those regions. An ``ideal'' eternal observer would then witness an infinite succession of cycles from false vacuum to true, and back. Within each cycle, the entire history of a hot universe would be replayed. If there were several minima of the inflaton potential, our ideal observer would visit each one of these minima with a frequency which depends on the shape of the potential. We generalize the formalism of stochastic inflation to analyze the global structure of the universe when this `recycling' process is taken into account.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | If the effective cosmological constant is non-zero, our observable universe may enter a stage of exponential expansion. | background 1.00 | 0.08 | 0.08 | hedged possibility 1.00 |
| s1 | In such case, regions of it may tunnel back to the false vacuum of an inflaton scalar field, and inflation with a high expansion rate may resume in those regions. | background 0.88 | 0.09 | 0.08 | hedged possibility 0.98 |
| s2 | An ``ideal'' eternal observer would then witness an infinite succession of cycles from false vacuum to true, and back. | interpretation 0.41 | 0.09 | 0.18 | asserted 0.58 |
| s3 | Within each cycle, the entire history of a hot universe would be replayed. | interpretation 0.54 | 0.12 | 0.11 | asserted 0.80 |
| s4 | If there were several minima of the inflaton potential, our ideal observer would visit each one of these minima with a frequency which depends on the shape of the potential. | result 0.40 | 0.27 | 0.10 | hedged possibility 0.56 |
| s5 | We generalize the formalism of stochastic inflation to analyze the global structure of the universe when this `recycling' process is taken into account. | contribution 0.72 | 0.92 | 0.18 | asserted 0.94 |
What was examined, and what was not
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Figures
Showing 1 of the paper's 9 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:astro-ph/9707292 by the authors.
References
How the literature uses it
32 arXiv papers cite this in 52 sentences
Papers citing it · 39 sentences without a confident label
Uses its method or tool 2 papers
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The size distribution for bubbles of different kinds on the flat slices can be found using the formalism developed in Refs. [ref] .
Holographic multiverse and conformal invariance · Flat foliations · 0.99
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One can do this using comoving coordinates, which are not expanding during inflation [ref] .
Inflationary Cosmology · Inflationary multiverse, string theory landscape and the anthropic principle · 0.95
Cites it as background 11 papers
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False vacuum eternal inflation [ref] is currently the most studied model of the multiverse scenario.
Probability of Slowroll Inflation in the Multiverse · Introduction · 0.99
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Following the seminal papers by Garriga, Vilenkin and collaborators [ref] , cosmological evolution on the landscape is described by a Markov process.
Early-Time Measure in Eternal Inflation · Vacuum dynamics on the landscape · 0.86
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In the standard presentation, e.g. [ref] , the rate equations for a two-minimum landscape read [equation] where $κ_f$ and $κ_t$ are transition probabilities per unit proper time.
De Sitter Space Without Dynamical Quantum Fluctuations · Landscape Eternal Inflation · 0.81
Discussion
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