What can the observation of nonzero curvature tell us?

The eternally inflating multiverse provides a consistent framework to understand coincidences and fine-tuning in the universe. As such, it provides the possibility of finding another coincidence: if the amount of slow-roll inflation was only slightly more than the anthropic threshold, then spatial curvature might be measurable. We study this issue in detail, particularly focusing on the question: "If future observations reveal nonzero curvature, what can we conclude?" We find that whether an observable signal arises or not depends crucially on three issues: the cosmic history just before the observable inflation, the measure adopted to define probabilities, and the nature of the correlation between the tunneling and slow-roll parts of the potential. We find that if future measurements find positive curvature at \Omega_k < -10^-4, then the framework of the eternally inflating multiverse is excluded with high significance. If the measurements instead reveal negative curvature at \Omega_k > 10^-4, then we can conclude (1) diffusive (new or chaotic) eternal inflation did not occur in our immediate past; (2) our universe was born by a bubble nucleation; (3) the probability measure does not reward volume increase; and (4) the origin of the observed slow-roll inflation is an accidental feature of the potential, not due to a theoretical mechanism. Discovery of \Omega_k > 10^-4 would also give us nontrivial information about the correlation between tunneling and slow-roll; e.g. a strong correlation favoring large N would be excluded in certain measures. We also ask whether the current constraint on \Omega_k is consistent with multiverse expectations, finding that the answer is yes, except for certain cases. In the course of this work we were led to consider vacuum decay branching ratios, and found that it is more likely than one might guess that the decays are dominated by a single channel.Comment: 46 pages, 5 figures; reference updates and typo corrections arising from final Phys. Rev. D copy editin

What Makes Complex Systems Complex?

This paper explores some of the factors that make complex systems complex. We first examine the history of complex systems. It was Aristotle’s insight that how elements are joined together helps determine the properties of the resulting whole. We find (a) that scientific reductionism does not provide a sufficient explanation; (b) that to understand complex systems, one must identify and trace energy flows; and (c) that disproportionate causality, including global tipping points, are all around us. Disproportionate causality results from the wide availability of energy stores. We discuss three categories of emergent phenomena—static, dynamic, and adaptive—and recommend retiring the term emergent, except perhaps as a synonym for creative. Finally, we find that virtually all communication is stigmergic

The Eastward Enlargement of the Eurozone: The Shaping of Capital Markets

Capital Markets, Transition Economies, EMU

Slow dynamics, aging, and glassy rheology in soft and living matter

We explore the origins of slow dynamics, aging and glassy rheology in soft and living matter. Non-diffusive slow dynamics and aging in materials characterised by crowding of the constituents can be explained in terms of structural rearrangement or remodelling events that occur within the jammed state. In this context, we introduce the jamming phase diagram proposed by Liu and Nagel to understand the ergodic-nonergodic transition in these systems, and discuss recent theoretical attempts to explain the unusual, faster-than-exponential dynamical structure factors observed in jammed soft materials. We next focus on the anomalous rheology (flow and deformation behaviour) ubiquitous in soft matter characterised by metastability and structural disorder, and refer to the Soft Glassy Rheology (SGR) model that quantifies the mechanical response of these systems and predicts aging under suitable conditions. As part of a survey of experimental work related to these issues, we present x-ray photon correlation spectroscopy (XPCS) results of the aging of laponite clay suspensions following rejuvenation. We conclude by exploring the scientific literature for recent theoretical advances in the understanding of these models and for experimental investigations aimed at testing their predictions.Comment: 22 pages, 5 postscript figures; invited review aricle, to appear in special issue on soft matter in Solid State Communication

Can the Universe Create Itself?

The question of first-cause has troubled philosophers and cosmologists alike. Now that it is apparent that our universe began in a Big Bang explosion, the question of what happened before the Big Bang arises. Inflation seems like a very promising answer, but as Borde and Vilenkin have shown, the inflationary state preceding the Big Bang must have had a beginning also. Ultimately, the difficult question seems to be how to make something out of nothing. This paper explores the idea that this is the wrong question --- that that is not how the Universe got here. Instead, we explore the idea of whether there is anything in the laws of physics that would prevent the Universe from creating itself. Because spacetimes can be curved and multiply connected, general relativity allows for the possibility of closed timelike curves (CTCs). Thus, tracing backwards in time through the original inflationary state we may eventually encounter a region of CTCs giving no first-cause. This region of CTCs, may well be over by now (being bounded toward the future by a Cauchy horizon). We illustrate that such models --- with CTCs --- are not necessarily inconsistent by demonstrating self-consistent vacuums for Misner space and a multiply connected de Sitter space in which the renormalized energy-momentum tensor does not diverge as one approaches the Cauchy horizon and solves Einstein's equations. We show such a Universe can be classically stable and self-consistent if and only if the potentials are retarded, giving a natural explanation of the arrow of time. Some specific scenarios (out of many possible ones) for this type of model are described. For example: an inflationary universe gives rise to baby universes, one of which turns out to be itself. Interestingly, the laws of physics may allow the Universe to be its own mother.Comment: 48 pages, 8 figure