Measure Problem for Eternal and Non-Eternal Inflation

We study various probability measures for eternal inflation by applying their regularization prescriptions to models where inflation is not eternal. For simplicity we work with a toy model describing inflation that can interpolate between eternal and non-eternal inflation by continuous variation of a parameter. We investigate whether the predictions of four different measures (proper time, scale factor cutoff, stationary and causal {diamond}) change continuously with the change of this parameter. We will show that {only} for the stationary measure the predictions change continuously. For the proper-time and the scale factor cutoff, the predictions are strongly discontinuous. For the causal diamond measure, the predictions are continuous only if the stage of the slow-roll inflation is sufficiently long.Comment: 9 pages, 4 figure

Cosmological Higgs fields

We present a time-dependent solution to the coupled Einstein-Higgs equations for general Higgs-type potentials in the context of flat FRW cosmological models. Possible implications are discussed.Comment: 5 pages, no figures. Version to be published in Phys. Rev. Lett. Changes: references and citations added; introduction partly modified; expanded discussion of relations between parameters in the Higgs potentia

A Toy Model for Open Inflation

The open inflation scenario based on the theory of bubble formation in the models of a single scalar field suffered from a fatal defect. In all the versions of this scenario known so far, the Coleman-De Luccia instantons describing the creation of an open universe did not exist. We propose a simple one-field model where the CDL instanton does exist and the open inflation scenario can be realized.Comment: 7 pages, 4 figures, revtex, a discussion of density perturbations is extende

Unambiguous probabilities in an eternally inflating universe

``Constants of Nature'' and cosmological parameters may in fact be variables related to some slowly-varying fields. In models of eternal inflation, such fields will take different values in different parts of the universe. Here I show how one can assign probabilities to values of the ``constants'' measured by a typical observer. This method does not suffer from ambiguities previously discussed in the literature.Comment: 7 pages, Final version (minor changes), to appear in Phys. Rev. Let

Inflation with Ω≠1\Omega \not = 1

We discuss various models of inflationary universe with $\Omega \not = 1$. A homogeneous universe with $\Omega > 1$ may appear due to creation of the universe "from nothing" in the theories where the effective potential becomes very steep at large $\phi$, or in the theories where the inflaton field $\phi$ nonminimally couples to gravity. Inflation with $\Omega < 1$ generally requires intermediate first order phase transition with the bubble formation, and with a second stage of inflation inside the bubble. It is possible to realize this scenario in the context of a theory of one scalar field, but typically it requires artificially bent effective potentials and/or nonminimal kinetic terms. It is much easier to obtain an open universe in the models involving two scalar fields. However, these models have their own specific problems. We propose three different models of this type which can describe an open homogeneous inflationary universe.Comment: 29 pages, LaTeX, parameters of one of the models are slightly modifie

Dynamical renormalization group methods in theory of eternal inflation

Dynamics of eternal inflation on the landscape admits description in terms of the Martin-Siggia-Rose (MSR) effective field theory that is in one-to-one correspondence with vacuum dynamics equations. On those sectors of the landscape, where transport properties of the probability measure for eternal inflation are important, renormalization group fixed points of the MSR effective action determine late time behavior of the probability measure. I argue that these RG fixed points may be relevant for the solution of the gauge invariance problem for eternal inflation.Comment: 11 pages; invited mini-review for Grav.Cos

Topological Defects as Seeds for Eternal Inflation

We investigate the global structure of inflationary universe both by analytical methods and by computer simulations of stochastic processes in the early Universe. We show that the global structure of the universe depends crucially on the mechanism of inflation. In the simplest models of chaotic inflation the Universe looks like a sea of thermalized phase surrounding permanently self-reproducing inflationary domains. In the theories where inflation occurs near a local extremum of the effective potential corresponding to a metastable state, the Universe looks like de Sitter space surrounding islands of thermalized phase. A similar picture appears even if the state $\phi = 0$ is unstable but the effective potential has a discrete symmetry $\phi \to =-\phi$. In this case the Universe becomes divided into domains containing different phases. These domains will be separated from each other by domain walls. However, unlike ordinary domain walls, these domain walls will inflate, and their thickness will exponentially grow. In the theories with continuous symmetries inflation generates exponentially expanding strings and monopoles surrounded by thermalized phase. Inflating topological defects will be stable, and they will unceasingly produce new inflating topological defects. This means that topological defects may play a role of indestructible seeds for eternal inflation.Comment: 21 pages, 17 figures (not included), Stanford University preprint SU--ITP--94--

Linguistic methodology for the analysis of aviation accidents

A linguistic method for the analysis of small group discourse, was developed and the use of this method on transcripts of commercial air transpot accidents is demonstrated. The method identifies the discourse types that occur and determine their linguistic structure; it identifies significant linguistic variables based upon these structures or other linguistic concepts such as speech act and topic; it tests hypotheses that support significance and reliability of these variables; and it indicates the implications of the validated hypotheses. These implications fall into three categories: (1) to train crews to use more nearly optimal communication patterns; (2) to use linguistic variables as indices for aspects of crew performance such as attention; and (3) to provide guidelines for the design of aviation procedures and equipment, especially those that involve speech

Volume Weighted Measures of Eternal Inflation in the Bousso-Polchinski Landscape

We consider the cosmological dynamics associated with volume weighted measures of eternal inflation, in the Bousso-Polchinski model of the string theory landscape. We find that this measure predicts that observers are most likely to find themselves in low energy vacua with one flux considerably larger than the rest. Furthermore, it allows for a satisfactory anthropic explanation of the cosmological constant problem by producing a smooth, and approximately constant, distribution of potentially observable values of Lambda. The low energy vacua selected by this measure are often short lived. If we require anthropically acceptable vacua to have a minimum life-time of 10 billion years, then for reasonable parameters a typical observer should expect their vacuum to have a life-time of approximately 12 billion years. This prediction is model dependent, but may point toward a solution to the coincidence problem of cosmology.Comment: 35 pages, 8 figure

STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY

In Brans-Dicke theory the Universe becomes divided after inflation into many exponentially large domains with different values of the effective gravitational constant. Such a process can be described by diffusion equations for the probability of finding a certain value of the inflaton and dilaton fields in a physical volume of the Universe. For a typical chaotic inflation potential, the solutions for the probability distribution never become stationary but grow forever towards larger values of the fields. We show here that a non-minimal conformal coupling of the inflaton to the curvature scalar, as well as radiative corrections to the effective potential, may provide a dynamical cutoff and generate stationary solutions. We also analyze the possibility of large nonperturbative jumps of the fluctuating inflaton scalar field, which was recently revealed in the context of the Einstein theory. We find that in the Brans--Dicke theory the amplitude of such jumps is strongly suppressed.Comment: 19 pages, LaTe