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

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--

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

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

Predictability crisis in inflationary cosmology and its resolution

Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated in the literature. Because of the infinite thermalized volume resulting from eternal inflation, it has proven difficult to obtain a meaningful and unambiguous probability distribution for observables, in particular due to the gauge dependence. In the present paper, we further develop the gauge-invariant procedure proposed in a previous work for models with a continuous variation of "constants". The recipe uses an unbiased selection of a connected piece of the thermalized volume as sample for the probability distribution. To implement the procedure numerically, we develop two methods applicable to a reasonably wide class of models: one based on the Fokker-Planck equation of stochastic inflation, and the other based on direct simulation of inflationary spacetime. We present and compare results obtained using these methods.Comment: 23 pages, 13 figure

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

From satisfaction to expectation: The patient's perspective in lower limb prosthetic care

Neck pain is a common musculoskeletal complaint and a relationship with reduced work-related functional capacity is assumed. A validated instrument to test functional capacity of patients with neck pain is unavailable. The objective of this study was to develop a Functional Capacity Evaluation (FCE), which is content valid for determining functional capacity in patients with work related neck disorders (WRND). A review of epidemiological review literature was conducted to identify physical risk factors for WRND. Evidence was found that physical risk factors contribute in development of WRND. Physical risk factors were related to repetitive movements, forceful movements, awkward positions and static contractions of the neck or the neck/shoulder region. An FCE was designed based on the risk factors identified. Eight tests were selected to cover all risk factors: repetitive side reaching, repetitive reaching overhead, static overhead work, front carry, forward static bend neck, overhead lift and the neck strength test. Content validity of this FCE was established by providing the rationale, specific objectives and operational definitions of the FCE. Further research is needed to establish reliability and other aspects of validity of the neck-FCE Aim Worldwide, family- centred and co- ordinated care are seen as the two most desirable and effective methods of paediatric care delivery. This study outlines current views on how team collaboration comprising professionals in paediatric rehabilitation and special education and the parents of children with disabilities should be organized, and analyses the policies of five paediatric rehabilitation settings associated with the care of 44 children with cerebral palsy ( CP) in the Netherlands. Methods For an overview of current ideas on collaboration, written statements of professional associations in Dutch paediatric rehabilitation were examined. The policy statements of the five participating settings were derived from their institutional files. Documents detailing the collaborative arrangements involving the various professionals and parents were evaluated at the institutional level and at the child level. Involvement of the stakeholders was analysed based on team conferences. Results Also in the Netherlands collaboration between rehabilitation and education professionals and parents is endorsed as the key principle in paediatric rehabilitation, with at its core the team conference in which the various priorities and goals are formulated and integrated into a personalized treatment plan. As to their collaborative approaches between rehabilitation centre and school, the five paediatric settings rarely differed, but at the child level approaches varied. Teams were large ( averaging 10.5 members), and all three stakeholder groups were represented, but involvement differed per setting, as did the roles and contributions of the individual team members. Conclusion Collaboration between rehabilitation and education professionals and parents is supported and encouraged nationwide. Views on collaboration have been formulated, and general guidelines on family- centred and co- ordinated care are available. Yet, collaborative practices in Dutch paediatric care are still developing. Protocols that carefully delineate the commitments to collaborate and that translate the policies into practical, detailed guidelines are needed, as they are a prerequisite for successful teamwork

Stationarity of Inflation and Predictions of Quantum Cosmology

We describe several different regimes which are possible in inflationary cosmology. The simplest one is inflation without self-reproduction of the universe. In this scenario the universe is not stationary. The second regime, which exists in a broad class of inflationary models, is eternal inflation with the self-reproduction of inflationary domains. In this regime local properties of domains with a given density and given values of fields do not depend on the time when these domains were produced. The probability distribution to find a domain with given properties in a self-reproducing universe may or may not be stationary, depending on the choice of an inflationary model. We give examples of models where each of these possibilities can be realized, and discuss some implications of our results for quantum cosmology. In particular, we propose a new mechanism which may help solving the cosmological constant problem.Comment: 30 pages, Stanford preprint SU-ITP-94-24, LaTe