  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 axio-dilaton, 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-BPS 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.

High Energy Physics - Theory