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

Towards the Theory of Cosmological Phase Transitions

We discuss recent progress (and controversies) in the theory of finite temperature phase transitions. This includes the structure of the effective potential at a finite temperature, the infrared problem in quantum statistics of gauge fields, the theory of formation of critical and subcritical bubbles and the theory of bubble wall propagation.Comment: 50 p

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

Role and Specificity of LGI4-ADAM22 Interactions in Peripheral Nerve Myelination

In the peripheral nervous system, large caliber axons are ensheathed and myelinated by Schwann cells. Myelin is crucial for a faster signal transduction along the nerve. Hence it is not surprising that defects in this myelination process cause serious neurological disease. Despite the medical importance of these cells, our understanding of the cellular and molecular mechanisms that control Schwann cell development and myelination is still incomplete. Continuous communication between Schwann cells and neurons is essential for the development, differentiation and myelination of peripheral nerves. Previous studies showed that LGI4 is a secreted protein that is crucial for myelination and might be a key player in this communication process. The main aim of this thesis is to elucidate the mechanism of LGI4 function in peripheral nerve myelination and to identify its interaction partners. Chapter 1 of this thesis presents an overview of the different types of cells in the peripheral nervous system with an emphasis on Schwann cell development and myelination

Islands in the landscape

The string theory landscape consists of many metastable de Sitter vacua, populated by eternal inflation. Tunneling between these vacua gives rise to a dynamical system, which asymptotically settles down to an equilibrium state. We investigate the effects of sinks to anti-de Sitter space, and show how their existence can change probabilities in the landscape. Sinks can disturb the thermal occupation numbers that would otherwise exist in the landscape and may cause regions that were previously in thermal contact to be divided into separate, thermally isolated islands.Comment: 31 pages, 8 figure

Thermal background can solve the cosmological moduli problem

It is shown that the coherent field oscillation of moduli fields with weak or TeV scale masses can dissipate its energy efficiently if they have a derivative coupling to standard bosonic fields in a thermal state. This mechanism may provide a new solution to the cosmological moduli problem in some special situations.Comment: 4 pages. revised versio

Open inflation in the landscape

Open inflation scenario is attracting a renewed interest in the context of string landscape. Since there are a large number of metastable de Sitter vacua in string landscape, tunneling transitions to lower metastable vacua through the bubble nucleation occur quite naturally. Although the deviation of Omega_0 from unity is small by the observational bound, we argue that the effect of this small deviation on the large angle CMB anisotropies can be significant for tensor-type perturbation in open inflation scenario. We consider the situation in which there is a large hierarchy between the energy scale of the quantum tunneling and that of the slow-roll inflation in the nucleated bubble. If the potential just after tunneling is steep enough, a rapid-roll phase appears before the slow-roll inflation. In this case the power spectrum is basically determined by the Hubble rate during the slow-roll inflation. If such rapid-roll phase is absent, the power spectrum keeps the memory of the high energy density there in the large angular components. The amplitude of large angular components can be enhanced due to the effects of the wall fluctuation mode if the bubble wall tension is small. Therefore, one can construct some models in which the deviation of Omega_0 from unity is large enough to produce measurable effects. We also consider a more general class of models, where the false vacuum decay may occur due to Hawking-Moss tunneling, as well as the models involving more than one scalar field. We discuss scalar perturbations in these models and point out that a large set of such models is already ruled out by observational data, unless there was a very long stage of slow-roll inflation after the tunneling. These results show that observational data allow us to test various assumptions concerning the structure of the string theory potentials and the duration of the last stage of inflation.Comment: 14 pages, 11 figures, v2:minor corrections and a reference added, v3:accepted for publication in PR

Creation of a Compact Topologically Nontrivial Inflationary Universe

If inflation can occur only at the energy density V much smaller than the Planck density, which is the case for many inflationary models based on string theory, then the probability of quantum creation of a closed or an infinitely large open inflationary universe is exponentially suppressed for all known choices of the wave function of the universe. Meanwhile under certain conditions there is no exponential suppression for creation of topologically nontrivial compact flat or open inflationary universes. This suggests, contrary to the standard textbook lore, that compact flat or open universes with nontrivial topology should be considered a rule rather than an exception.Comment: 9 pages 2 figures, new materials and references adde

Reheating after Inflation

The theory of reheating of the Universe after inflation is developed. The transition from inflation to the hot Universe turns out to be strongly model-dependent and typically consists of several stages. Immediately after inflation the field $\phi$ begins rapidly rolling towards the minimum of its effective potential. Contrary to some earlier expectations, particle production during this stage does not lead to the appearance of an extra friction term $\Gamma\dot\phi$ in the equation of motion of the field $\phi$. Reheating becomes efficient only at the next stage, when the field $\phi$ rapidly oscillates near the minimum of its effective potential. We have found that typically in the beginning of this stage the classical inflaton field $\phi$ very rapidly (explosively) decays into $\phi$-particles or into other bosons due to broad parametric resonance. This stage cannot be described by the standard elementary approach to reheating based on perturbation theory. The bosons produced at this stage, as well as some part of the classical field $\phi$ which survives the stage of explosive reheating, should further decay into other particles, which eventually become thermalized. The last stages of decay can be described in terms of perturbation theory. Complete reheating is possible only in those theories where a single massive $\phi$-particle can decay into other particles. This imposes strong constraints on the structure of inflationary models. On the other hand, this means that a scalar field can be a cold dark matter candidate even if it is strongly coupled to other fields.Comment: 7 pages, 1 figure, LaTeX, UH-IfA-94/35; SU-ITP-94-13; YITP/U-94-15 (paper replaced by its version to be published in Phys. Rev. Lett.

Dynamics of Symmetry Breaking and Tachyonic Preheating

We reconsider the old problem of the dynamics of spontaneous symmetry breaking using 3d lattice simulations, and develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential. As an application of this theory we consider preheating in the hybrid inflation scenario, including SUSY-motivated F-term and D-term inflationary models. We show that preheating in hybrid inflation is typically tachyonic and the stage of oscillations of a homogeneous component of the scalar fields driving inflation ends after a single oscillation. Our results may also be relevant for the theory of the formation of disoriented chiral condensates in heavy ion collisions.Comment: 7 pages, 6 figures. Higher quality figures and computer generated movies in gif format illustrating our results can be found at http://physics.stanford.edu/gfelder/hybri