[1] Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations (in the form of lumps or streaks) in average energy and wave action distributions. These variations explicitly survive averaging over wavelength and wave propagation direction. The lumps and streaks in average local action mean that the uniform sampling assumed in the venerable Longuet-Higgins theory does not apply. Proper handling of the nonuniform sampling results in greatly increased probability of freak wave formation. The present theory represents a synthesis of Longuet-Higgins Gaussian seas and the refraction model of White and Fornberg, which used a nonGaussian nonstatistical plane wave incident seaway. Using the linearized equations for deep ocean waves, we obtain quantitative predictions for the increased probability of freak wave formation when the refractive effects are taken into account. The wave height distribution depends primarily on the ''freak index,'' g, which measures the strength of refraction relative to the angular spread of the incoming sea. Dramatic effects are obtained in the tail of this distribution even for the modest values of the freak index that are expected to occur commonly in nature. Extensive comparisons are made between the analytical description and numerical simulations.

Nothing-the absence of spacetime-can be either an endpoint of tunneling, as in the bubble of nothing, or a starting point for tunneling, as in the quantum creation of a universe. We argue that these two tunnelings can be treated within a unified framework, and that, in both cases, nothing should be thought of as the limit of anti-de Sitter space in which the curvature length approaches zero. To study nothing, we study decays in models with perturbatively stabilized extra dimensions, which admit not just bubbles of nothing-topology-changing transitions in which the extra dimensions pinch off and a hole forms in spacetime-but also a whole family of topology-preserving transitions that nonetheless smoothly hollow out and approach the bubble of nothing in one limit. The bubble solutions that are close to this limit, bubbles of next-tonothing, give us a controlled setting in which to understand nothing. Armed with this understanding, we are able to embed proposed mechanisms for the reverse process, tunneling from nothing to something, within the relatively secure foundation of the Coleman-De Luccia formalism and show that the Hawking-Turok instanton does not mediate the quantum creation of a universe.

The rate and manner of vacuum decay are calculated in an explicit flux compactification, including all thick-wall and gravitational effects. For landscapes built of many units of a single flux, the fastest decay is usually to discharge just one unit. By contrast, for landscapes built of a single unit each of many different fluxes, the fastest decay is usually to discharge all the flux at once, which destabilizes the radion and begets a bubble of nothing. By constructing the bubble of nothing as the limit in which ever more flux is removed, we gain new insight into the bubble's appearance. Finally, we describe a new instanton that mediates simultaneous flux tunneling and decompactification. Our model is the thin-brane approximation to six-dimensional Einstein-Maxwell theory.

For landscapes of field theory vacua, we identify an effect that can greatly enhance the decay rates to wildly distant minima-so much so that such transitions may dominate over transitions to near neighbors. We exhibit these 'giant leaps' in both a toy two-field model and, in the thin-wall limit, amongst the four-dimensional vacua of 6D Einstein-Maxwell theory, and it is argued that they are generic to landscapes arising from flux compactifications. We discuss the implications for the cosmological constant and the stability of stringy de Sitter.

Every de Sitter vacuum can transition to every other de Sitter vacuum despite any obstacle, despite intervening anti-de Sitter sinks, despite not being connected by an instanton. Eternal inflation populates the whole landscape.

We study the spectrum and perturbative stability of Freund-Rubin compactifications on M p × M N q , where M N q is itself a product of N q-dimensional Einstein manifolds. The higher-dimensional action has a cosmological term Λ and a q-form flux, which individually wraps each element of the product; the extended dimensions M p can be anti-de Sitter, Minkowski, or de Sitter. We find the masses of every excitation around this background, as well as the conditions under which these solutions are stable. This generalizes previous work on Freund-Rubin vacua, which focused on the N = 1 case, in which a q-form flux wraps a single q-dimensional Einstein manifold. The N = 1 case can have a classical instability when the q-dimensional internal manifold is a product-one of the members of the product wants to shrink while the rest of the manifold expands. Here, we will see that individually wrapping each element of the product with a lower-form flux cures this cycle-collapse instability. The N = 1 case can also have an instability when Λ > 0 and q ≥ 4 to shape-mode perturbations; we find the same instability in compactifications with general N , and show that it even extends to cases where Λ ≤ 0. On the other hand, when q = 2 or 3, the shape modes are always stable and there is a broad class of AdS and de Sitter vacua that are perturbatively stable to all fluctuations.

Instantons are tunneling solutions that connect two vacua, and under a small change in the potential, instantons sometimes disappear. We classify these disappearances as smooth (decay rate → 0 at disappearance) or abrupt (decay rate = 0 at disappearance). Abrupt disappearances mean that a small change in the parameters can produce a drastic change in the physics, as some states become suddenly unreachable. The simplest abrupt disappearances are associated with annihilation by another Euclidean solution with higher action and one more negative mode; higher-order catastrophes can occur in cases of enhanced symmetry. We study a few simple examples, including the 6D Einstein-Maxwell theory, and give a unified account of instanton disappearances.

There is a standard story about decay in multi-dimensional flux landscapes: that from any state, the fastest decay is to take a small step, discharging one flux unit at a time; that fluxes with the same coupling constant are interchangeable; and that states with N units of a given flux have the same decay rate as those with −N . We show that this standard story is false. The fastest decay is a giant leap that discharges many different fluxes in unison; this decay is mediated by a 'minimal' brane that wraps the internal manifold and exhibits behavior not visible in the effective theory. We discuss the implications for the cosmological constant.