New local duals in eternal inflation

Bousso, Raphael; Katz, Dan Mainemer

doi:10.1103/physrevd.86.083530

Cited by 7 publications

(11 citation statements)

References 43 publications

(85 reference statements)

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“…7 The evaluation of the measure may be further complicated in realistic models where the boundaries of MðÞ might be rugged and fractal-like. In future work [45] it will be shown that the new scale factor cutoff is equivalent to a local measure, where such issues do not arise. More generally, the evaluation of global measures is usually dramatically simplified by considering local duals, due to the elimination of the infinitely redundant exponential self-reproduction underlying the attractor regime.…”

Section: Rate Equationmentioning

confidence: 99%

New scale factor measure

Bousso

2012

Phys. Rev. D

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The computation of probabilities in an eternally inflating universe requires a regulator or ''measure.'' The scale factor time measure truncates the Universe when a congruence of timelike geodesics has expanded by a fixed volume factor. This definition breaks down if the generating congruence is contracting-a serious limitation that excludes from consideration gravitationally bound regions such as our own. Here we propose a closely related regulator which is well defined in the entire spacetime. The new scale factor cutoff restricts to events with a scale factor below a given value. Since the scale factor vanishes at caustics and crunches, this cutoff always includes an infinite number of disconnected future regions. We show that this does not lead to divergences. The resulting measure combines desirable features of the old scale factor cutoff and of the light-cone time cutoff, while eliminating some of the disadvantages of each.

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Section: Rate Equationmentioning

confidence: 99%

New scale factor measure

Bousso

2012

Phys. Rev. D

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“…For instance, the scalefactor, light-cone time and CAH+ cutoffs are dual to the local "fat geodesic", causal patch, and Hubbletube cutoffs, respectively [5,11,18]. This duality holds for a very specific choice of initial conditions for the local measures, with probabilities given by the dominant eigenvector of the rate equation for eternal inflation.…”

Section: Dominant Eigenvector Initial Conditionsmentioning

confidence: 99%

“…Essentially the same rate equation holds for the light-cone time cutoff, which is dual to the causal patch [11].…”

Section: A Rate Equationmentioning

confidence: 99%

“…Several of the most attractive measure proposals are related by global-local duality [11]. For instance, the scalefactor, light-cone time and CAH+ cutoffs are dual to the local "fat geodesic", causal patch, and Hubbletube cutoffs, respectively [5,11,18].…”

Section: Dominant Eigenvector Initial Conditionsmentioning

confidence: 99%

“…Here, we use the causal patch measure [8,9]. Closely related local measures, such as the fat geodesic [5,10] or the Hubbletube [11] are equivalent for the purpose of the (relatively crude) question of whether an arrow of time is predicted. Finally, there also exist global measures, such as light-cone time [17][18][19] and scale factor time [20].…”

Section: Introductionmentioning

confidence: 99%

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Multivacuum initial conditions and the arrow of time

Bousso

Zukowski

2013

Phys. Rev. D

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Depending on the type and arrangement of metastable vacua in the theory, initial conditions in a de Sitter vacuum with arbitrarily large entropy can be compatible with the observed arrow of time, if the causal patch or related measures are used to regulate divergences. An important condition, however, is that the initial vacuum cannot produce observers from rare fluctuations (Boltzmann brains). Here we consider more general initial conditions where multiple vacua have nonzero initial probability. We examine whether the prediction of an arrow of time is destroyed by a small initial admixture of vacua that can produce Boltzmann brains. We identify general criteria and apply them to two nontrivial examples of such initial probability distributions. The Hartle-Hawking state is superexponentially dominated by the vacuum with smallest positive cosmological constant, so one might expect that other initial vacua can be neglected; but in fact, their inclusion drastically narrows the range of theory parameters for which an arrow of time is predicted. The dominant eigenvector of the global rate equation of eternal inflation is dominated by the longest-lived metastable vacuum. If an arrow of time emerges in the single-initial-vacuum approximation, then we find that this conclusion survives the admixture of other initial vacua. By global-local measure duality, this result amounts to a successful consistency test of certain global cutoffs, including light-cone time and scale-factor time.

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Bayesian reasoning in eternal inflation: A solution to the measure problem

Khoury

Wong

2023

Phys. Rev. D

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New local duals in eternal inflation

Cited by 7 publications

References 43 publications

New scale factor measure

New scale factor measure

Multivacuum initial conditions and the arrow of time

Bayesian reasoning in eternal inflation: A solution to the measure problem

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