In this dissertation we study two topics in Theoretical Cosmology: one more formal, the other more phenomenological. We work in the context of eternally inflating cosmologies. These arise in any fundamental theory that contains at least one stable or metastable de Sitter vacuum. Each topic is presented in a different chapter:
Chapter 1 deals with the measure problem in eternal inflation. Global-local duality is the equivalence of seemingly different regulators in eternal inflation. For example, the light- cone time cutoff (a global measure, which regulates time) makes the same predictions as the causal patch (a local measure that cuts off space). We show that global-local duality is far more general. It rests on a redundancy inherent in any global cutoff: at late times, an attractor regime is reached, characterized by the unlimited exponential self-reproduction of a certain fundamental region of spacetime. An equivalent local cutoff can be obtained by restricting to this fundamental region. We derive local duals to several global cutoffs of interest. The New Scale Factor Cutoff is dual to the Short Fat Geodesic, a geodesic of fixed infinitesimal proper width. Vilenkin’s CAH Cutoff is equivalent to the Hubbletube, whose width is proportional to the local Hubble volume. The famous youngness problem of the Proper Time Cutoff can be readily understood by considering its local dual, the Incredible Shrinking Geodesic. The chapter closely follows our paper [1].
Chapter 2 deals with the question of whether neutrino masses could be anthropically explained. The sum of active neutrino masses is well constrained, 58 meV ≤ mν 0.23 eV, but the origin of this scale is not well understood. Here we investigate the possibility that it arises by environmental selection in a large landscape of vacua. Earlier work had noted the detrimental effects of neutrinos on large scale structure. However, using Boltzmann codes to compute the smoothed density contrast on Mpc scales, we find that dark matter halos form abundantly for mν 10eV. This finding rules out an anthropic origin of mν, unless a different catastrophic boundary can be identified. Here we argue that galaxy formation becomes inefficient for mν 10 eV. We show that in this regime, structure forms late and is dominated by cluster scales, as in a top-down scenario. This is catastrophic: baryonic gas will cool too slowly to form stars in an abundance comparable to our universe. With this novel cooling boundary, we find that the anthropic prediction for mν agrees at better than 2σ with current observational bounds. A degenerate hierarchy is mildly preferred. The chapter closely follows our paper [2] .
