Properties of the scale factor measure

Bousso, Raphael; Freivogel, Ben; Yang, I-Sheng

doi:10.1103/physrevd.79.063513

Cited by 98 publications

(197 citation statements)

References 58 publications

(163 reference statements)

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“…We have largely avoided discussing deep issues involving the initial conditions for inflation, including the global view of eternal inflation [822][823][824][825], the associated measure problem [826][827][828][829][830][831][832][833], and the geodesic incompleteness of inflation in the past [834]. String theory has inspired several compelling approaches to these questions, but no complete solutions have been advanced.…”

Section: Discussionmentioning

confidence: 99%

Inflation and String Theory

2015

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Section: Discussionmentioning

confidence: 99%

Inflation and String Theory

2015

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“…This section is rather technical and readers who are not measure enthusiasts are welcome to skip it. Similar computations have been done for other slicings in [39,38,26,40,37], but we will use geometric tricks to simplify these analyses and obtain some nice "exact" results. We will assume that decay rates are small enough that the bubble nucleates well after its ancestor and thus that the light-cone time is comoving inside of the ancestor.…”

Section: A3 Light-cone Time In a Bubblementioning

confidence: 99%

“…It has been understood for a while that the existence of terminal vacua changes the story in a very positive direction [24,25,26], and the sharpest statement of these ideas is in a recent paper by Bousso [27]. The relevant mechanism is simply illustrated in the cellular model.…”

Section: Time's Arrow Terminals and Fractal Flowsmentioning

confidence: 99%

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Tree-like structure of eternal inflation: A solvable model

et al. 2012

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In this paper we introduce a simple discrete stochastic model of eternal inflation that shares many of the most important features of the continuum theory as it is now understood. The model allows us to construct a multiverse and rigorously analyze its properties. Although simple and easy to solve, it has a rich mathematical structure underlying it. Despite the discreteness of the space-time the theory exhibits an unexpected non-perturbative analog of conformal symmetry that acts on the boundary of the geometry. The symmetry is rooted in the mathematical properties of trees, p-adic numbers, and ultrametric spaces; and in the physical property of detailed balance. We provide self-contained elementary explanations of the unfamiliar mathematical concepts, which have have also appeared in the study of the p-adic string.The symmetry acts on a huge collection of very low dimensional "multiverse fields" that are not associated with the usual perturbative degrees of freedom. They are connected with the late-time statistical distribution of bubble-universes in the multiverse.The conformal symmetry which acts on the multiverse fields is broken by the existence of terminal decays-to hats or crunches-but in a particularly simple way. We interpret this symmetry breaking as giving rise to an arrow of time.The model is used to calculate statistical correlations at late time and to discuss the measure problem. We show that the natural cutoff in the model is the analog of the so-called light-cone-time cutoff. Applying the model to the problem of the cosmological constant, we find agreement with earlier work.

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“…The picture of the multiverse from a local viewpoint, which arises here as a consequence of quantum mechanics, has been promoted in the context of geometric cutoff measures; see Refs. [33][34][35] for example.…”

confidence: 99%

Quantum Mechanics, Spacetime Locality, and Gravity

Nomura

2013

Found Phys

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Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are related with each other, developing a picture for quantum measurement and cosmological histories in the quantum mechanical universe. In order to describe the cosmological dynamics correctly within the full quantum mechanical context, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the "observer dependence" of horizons/spacetime-these phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincaré transformation in the quantum gravitational context. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanics-it evolves deterministically and unitarily. The beginning of the multiverse, however, is still an open issue.

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Properties of the scale factor measure

Cited by 98 publications

References 58 publications

Inflation and String Theory

Inflation and String Theory

Tree-like structure of eternal inflation: A solvable model

Quantum Mechanics, Spacetime Locality, and Gravity

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