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An eternally inflating universe produces an infinite amount of spatial volume, so every possible event happens an infinite number of times, and it is impossible to define probabilities in terms of frequencies. This problem is usually addressed by means of a measure, which regulates the infinities and produces meaningful predictions. I argue that any measure should obey certain general axioms, but then give a simple toy model in which one can prove that no measure obeying the axioms exists. In certain cases of eternal inflation there are measures that obey the axioms, but all such measures appear to be unacceptable for other reasons. Thus the problem of defining sensible probabilities in eternal inflation seems not be solved.
Magnetic monopoles have been a subject of study for more than a century since the first ideas by A. Vaschy and P. Curie, circa 1890. In 1974, Y. Nambu proposed a model for magnetic monopoles exploring a parallelism between the broken symmetry Higgs a
In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that we live at
We model the essential features of eternal inflation on the landscape of a dense discretuum of vacua by the potential $V(phi)=V_{0}+delta V(phi)$, where $|delta V(phi)|ll V_{0}$ is random. We find that the diffusion of the distribution function $rho(
We present an interpretation of the physics of space-times undergoing eternal inflation by repeated nucleation of bubbles. In many cases the physics can be interpreted in terms of the quantum mechanics of a system with a finite number of states. If t
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixin