12,517 research outputs found
Inflation and Eternal Inflation
The basic workings of inflationary models are summarized, along with the
arguments that strongly suggest that our universe is the product of inflation.
The mechanisms that lead to eternal inflation in both new and chaotic models
are described. Although the infinity of pocket universes produced by eternal
inflation are unobservable, it is argued that eternal inflation has real
consequences in terms of the way that predictions are extracted from
theoretical models. The ambiguities in defining probabilities in eternally
inflating spacetimes are reviewed, with emphasis on the youngness paradox that
results from a synchronous gauge regularization technique. Vilenkin's proposal
for avoiding these problems is also discussed.Comment: 27 pages, including 5 figures, LaTeX (elsart macros for Physics
Reports, included). To be published in the David Schramm Memorial Volume of
Physics Report
Volumes of balls in Riemannian manifolds and Uryson width
If is a closed Riemannian manifold where every unit ball has
volume at most (a sufficiently small constant), then the
-dimensional Uryson width of is at most 1.Comment: 26 page
A short proof of the multilinear Kakeya inequality
We give a short proof of a slightly weaker version of the multilinear Kakeya
inequality proven by Bennett, Carbery, and Tao.Comment: 7 pages, minor revision, accepted for publication in the Mathematical
Proceedings of the Cambridge Philosophical Societ
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