[Show abstract][Hide abstract] ABSTRACT: The non-perturbative instabilities of hot Kaluza-Klein spacetime are
investigated. In addition to the known instability of hot space (the nucleation
of 4D black holes) and the known instability of KK space (the nucleation of
bubbles of nothing by quantum tunneling), we find two new instabilities: the
nucleation of 5D black holes, and the nucleation of bubbles of nothing by
thermal fluctuation. These four instabilities are controlled by two Euclidean
instantons, with each instanton doing double duty via two inequivalent analytic
continuations; thermodynamic instabilities of one are shown to be related to
mechanical instabilities of the other. I also construct bubbles of nothing that
are formed by a hybrid process involving both thermal fluctuation and quantum
tunneling. There is an exact high-temperature/low-temperature duality that
relates the nucleation of black holes to the nucleation of bubbles of nothing.
Physical Review D 08/2014; 90(10). DOI:10.1103/PhysRevD.90.104017 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate a simple extra-dimensional model and its four-dimensional
vacua. This model has a two-form flux and a positive cosmological constant, and
the extra dimensions are compactified as the product of $N$ two-spheres. The
theory is an interesting laboratory because it is at once simple enough to be
soluble but rich enough to exhibit many features not present in previous model
landscapes.
Physical Review D 01/2014; 90(4). DOI:10.1103/PhysRevD.90.045016 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study compactifications of $D$-dimensional de Sitter space with a $q$-form
flux down to $D-Nq$ dimensions. We show that for $(N-1)(q-1)\geq 2$ there are
double-exponentially or even infinitely many compact de Sitter vacua, and that
their effective cosmological constants accumulate at zero. This population
explosion of $\Lambda \ll 1$ de Sitters arises by a mechanism analogous to
natural selection.
Physical Review D 11/2013; 90(12). DOI:10.1103/PhysRevD.90.124048 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the spectrum and perturbative stability of Freund-Rubin
compactifications on $M_p \times M_{Nq}$, where $M_{Nq}$ is itself a product of
$N$ $q$-dimensional Einstein manifolds. The higher-dimensional action has a
cosmological term $\Lambda$ 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 $\Lambda>0$ and $q\ge4$ to shape-mode perturbations; we find
the same instability in compactifications with general $N$, and show that it
even extends to cases where $\Lambda\le0$. 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.
Physical Review D 10/2013; 90(4). DOI:10.1103/PhysRevD.90.044047 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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-to-nothing, 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: There is a standard story about decay in multidimensional 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 problem.
[Show abstract][Hide abstract] ABSTRACT: 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 goes to 0 at disappearance) or abrupt
(decay rate not equal to 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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 approximation, 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. Comment: 23 pages, 12 figures