Field dynamics and tunneling in a flux landscape

We investigate field dynamics and tunneling between metastable minima in a landscape of type IIB flux compactifications, utilizing monodromies of the complex structure moduli space to continuously connect flux vacua. After describing the generic features of a flux-induced potential for the complex structure and type IIB axiodilaton, we specialize to the mirror quintic Calabi-Yau to obtain an example landscape. Studying the cosmological dynamics of the complex structure moduli, we find that the potential generically does not support slow-roll inflation and that in general the landscape separates neatly into basins of attraction of the various minima. We then discuss tunneling, with the inclusion of gravitational effects, in many-dimensional field spaces. A set of constraints on the form of the Euclidean paths through field space are presented, and then applied to construct approximate instantons mediating the transition between de Sitter vacua in the flux landscape. We find that these instantons are generically thick wall and that the tunneling rate is suppressed in the large-volume limit. We also consider examples where supersymmetry is not broken by fluxes, in which case near--Bogomolnyi-Prasad-Sommerfeld thin-wall bubbles can be constructed. We calculate the bubble-wall tension, finding that it scales like a D- or NS-brane bubble, and comment on the implications of this correspondence. Finally, we present a brief discussion of eternal inflation in the flux landscape.