Metastable vacuum
A false vacuum is a local minimum of a field potential that is not the global minimum. Classically the field can remain trapped. Quantum mechanically, a transition to a lower-energy configuration may occur through tunnelling.
Coleman–De Luccia decay
With gravity included, the semiclassical transition is described by an Euclidean bounce solution. The decay rate per unit volume has the schematic form Γ/V ≈ A exp(−B/ħ), where B is the difference between the Euclidean action of the bounce and the false-vacuum background. The exponential makes the rate extremely sensitive to the potential shape.
Hawking–Moss transitions
When the barrier and de Sitter curvature place the system in a different regime, the Hawking–Moss instanton provides another description: the field fluctuates to the top of the barrier over a Hubble-sized region and then evolves away from it. Which description applies is model dependent.
From a bubble to a cosmology
Nucleation is only the beginning. One must determine the bubble interior geometry, field evolution, possible period of slow-roll inflation inside the bubble, reheating, perturbations and whether the region produces a viable hot cosmology. A pretty bubble picture skips almost all of the hard physics.
What the landscape means
A “landscape” is a theory-space picture with multiple metastable vacua or effective low-energy configurations. It is not an observed astronomical map. Connecting a landscape to predictions requires transition rates, population dynamics, a measure prescription and a model for how observables depend on the vacuum.