Cosmic string scaling in flat space

We investigate the evolution of infinite strings as a part of a complete cosmic string network in flat space. We perform a simulation of the network which uses functional forms for the string position and thus is exact to the limits of computer arithmetic. Our results confirm that the wiggles on the strings obey a scaling law described by universal power spectrum. The average distance between long strings also scales accurately with the time. These results suggest that small-scale structure will also scale in expanding universe, even in the absence of gravitational damping.Comment: 13 pages,7 figure

Energy conditions outside a dielectric ball

We show analytically that the vacuum electromagnetic stress-energy tensor outside a ball with constant dielectric constant and permeability always obeys the weak, null, dominant, and strong energy conditions. There are still no known examples in quantum field theory in which the averaged null energy condition in flat spacetime is violated.Comment: 12 pages, RevTex

The quantum inequalities do not forbid spacetime shortcuts

A class of spacetimes (comprising the Alcubierre bubble, Krasnikov tube, and a certain type of wormholes) is considered that admits `superluminal travel' in a strictly defined sense. Such spacetimes (they are called `shortcuts' in this paper) were suspected to be impossible because calculations based on `quantum inequalities' suggest that their existence would involve Planck-scale energy densities and hence unphysically large values of the `total amount of negative energy' E_tot. I argue that the spacetimes of this type may not be unphysical at all. By explicit examples I prove that: 1) the relevant quantum inequality does not (always) imply large energy densities; 2) large densities may not lead to large values of E_tot; 3) large E_tot, being physically meaningless in some relevant situations, does not necessarily exclude shortcuts.Comment: Minor corrections and addition

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

Prediction and explanation in the multiverse

Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical? There is a widespread belief that this question is inherently vague, and that there are various possible choices for the types of reference objects which should be counted in. Here we argue that the ``ideal'' reference class (for the purpose of making predictions) can be defined unambiguously in a rather precise way, as the set of all observers with identical information content. When the observers in a given class perform an experiment, the class branches into subclasses who learn different information from the outcome of that experiment. The probabilities for the different outcomes are defined as the relative numbers of observers in each subclass. For practical purposes, wider reference classes can be used, where we trace over all information which is uncorrelated to the outcome of the experiment, or whose correlation with it is beyond our current understanding. We argue that, once we have gathered all practically available evidence, the optimal strategy for making predictions is to consider ourselves typical in any reference class we belong to, unless we have evidence to the contrary. In the latter case, the class must be correspondingly narrowed.Comment: Minor clarifications adde