Anthropic prediction for a large toy landscape

Olum, Ken D.; Schwartz-Perlov, Delia

doi:10.1088/1475-7516/2007/10/010

Cited by 29 publications

(53 citation statements)

References 38 publications

(93 reference statements)

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“…This exact spectrum requires diagonalizing an N × N matrix, which is computationally intensive for large N . A useful and intuitive approach is the "downward" approximation [90,91], which neglects upward transitions. To see how this is justified, recall the detailed balance condition (25).…”

Section: Downward Approximationmentioning

confidence: 99%

Search optimization, funnel topography, and dynamical criticality on the string landscape

Khoury

Parrikar

2019

J. Cosmol. Astropart. Phys.

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A striking feature of our universe is its near criticality. The cosmological constant and weak hierarchy problems, as well as the metastability of the electroweak vacuum, can all be understood as problems of criticality. This suggests a statistical physics approach, based on the landscape of string theory. In this paper we present a dynamical selection mechanism for hospitable vacua based on search optimization. Instead of focusing on late-time, stationary probability distributions for the different vacua, we are interested in the approach to equilibrium. This is particularly relevant if cosmological evolution on the multiverse has occurred for a finite time much shorter than the exponentially-long mixing time for the landscape. We argue this imposes a strong selection pressure among hospitable vacua, favoring those that lie in regions where the search algorithm is efficient. Specifically, we show that the mean first passage time is minimized for hospitable vacua lying at the bottom of funnel-like regions, akin to the smooth folding funnels of naturallyoccurring proteins and the convex loss functions of well-trained deep neural networks. The optimality criterion is time-reparametrization invariant and defined by two competing requirements: search efficiency, which requires minimizing the mean first passage time, and sweeping exploration, which requires that random walks are recurrent. Optimal landscape regions reach a compromise by lying at the critical boundary between recurrence and transience, thereby achieving dynamical criticality. Remarkably, this implies that the optimal lifetime of vacua coincides with the de Sitter Page time, τ crit ∼ M 2 Pl /H 3 . Our mechanism makes concrete phenomenological predictions: 1. The expected lifetime of our universe is 10 130 years, which is ∼ > 2σ from the Standard Model metastability estimate; 2. The supersymmetry breaking scale should be high, ∼ > 10 10 GeV. The present framework suggests a correspondence between the near-criticality of our universe and nonequilibrium critical phenomena on the landscape.

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Section: Downward Approximationmentioning

confidence: 99%

Search optimization, funnel topography, and dynamical criticality on the string landscape

Khoury

Parrikar

2019

J. Cosmol. Astropart. Phys.

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“…But considerable progress has been made by the more pedestrian method of elimination. The number of simple candidate measures is not large, and many make wrong predictions, which go by colorful names such as Q-catastrophe, youngness paradox, Boltzmann brain paradox, and staggering problem [56,[61][62][63][64][65][66][67][68][69]. But they just come down to an old-fashioned (and usually violent) conflict with observation.…”

Section: Dynamical Selection Effectsmentioning

confidence: 99%

The cosmological constant

2007

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The energy density of the vacuum, , is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that = 0 conflicts with observation. The possibility remains that is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.

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“…Depending on the details of the string landscape, the proposal may render most vacua dynamically inaccessible (the "staggering problem" of Refs. [23,24]). This would also amount to a conflict with observation, namely the prediction that we should observe a much larger cosmological constant with probability very close to 1.…”

Section: B the Measure Problem: A Phenomenological Approachmentioning

confidence: 99%

Boltzmann babies in the proper time measure

2008

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After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well-defined, and consistent with observation. This allows us to proceed by elimination. As an example, we consider the proper time cutoff on a geodesic congruence. It predicts that typical observers are quantum fluctuations in the early universe, or Boltzmann babies. We sharpen this well-known youngness problem by taking into account the expansion and open spatial geometry of pocket universes. Moreover, we relate the youngness problem directly to the probability distribution for observables, such as the temperature of the cosmic background radiation. We consider a number of modifications of the proper time measure, but find none that would make it compatible with observation.

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Anthropic prediction for a large toy landscape

Cited by 29 publications

References 38 publications

Search optimization, funnel topography, and dynamical criticality on the string landscape

Search optimization, funnel topography, and dynamical criticality on the string landscape

The cosmological constant

Boltzmann babies in the proper time measure

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