General bounds on holographic complexity

We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd’s bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

Black hole induced false vacuum decay from first principles

We provide a method to calculate the rate of false vacuum decay induced by a black hole. The method uses complex tunneling solutions and consistently takes into account the structure of different quantum vacua in the black hole metric via boundary conditions. The latter are connected to the asymptotic behavior of the time-ordered Green’s function in the corresponding vacua. We illustrate the technique on a two-dimensional toy model of a scalar field with inverted Liouville potential in an external background of a dilaton black hole. We analytically derive the exponential suppression of tunneling from the Boulware, Hartle-Hawking and Unruh vacua and show that they are parametrically different. The Unruh vacuum decay rate is exponentially smaller than the decay rate of the Hartle-Hawking state, though both rates become unsuppressed at high enough black hole temperature. We interpret the vanishing suppression of the Unruh vacuum decay at high temperature as an artifact of the two-dimensional model and discuss why this result can be modified in the realistic case of black holes in four dimensions.

Islands in multiverse models

We consider multiverse models in two-dimensional linear dilaton-gravity theories as toy models of false vacuum eternal inflation. Coupling conformal matter we calculate the Von Neumann entropy of subregions. When these are sufficiently large we find that an island develops covering most of the rest of the multiverse, leading to a Page-like transition. This resonates with a description of multiverse models in semiclassical quantum cosmology, where a measure for local predictions is given by saddle point geometries which coarse-grain over any structure associated with eternal inflation beyond one’s patch.

Correlated gravitational wave and microlensing signals of macroscopic dark matter

Fermion dark matter particles can aggregate to form extended dark matter structures via a first-order phase transition in which the particles get trapped in the false vacuum. We study Fermi balls created in a phase transition induced by a generic quartic thermal effective potential. We show that for Fermi balls of mass, 3 × 10−12M⊙ ≲ MFB ≲ 10−5M⊙, correlated observations of gravitational waves produced during the phase transition (at SKA/THEIA/μAres), and gravitational microlensing caused by Fermi balls (at Subaru-HSC), can be made.

Dark Matter as dark dwarfs and other macroscopic objects: multiverse relics?

First order phase transitions can leave relic pockets of false vacua and their particles, that manifest as macroscopic Dark Matter. We compute one predictive model: a gauge theory with a dark quark relic heavier than the confinement scale. During the first order phase transition to confinement, dark quarks remain in the false vacuum and get compressed, forming Fermi balls that can undergo gravitational collapse to stable dark dwarfs (bound states analogous to white dwarfs) near the Chandrasekhar limit, or primordial black holes.

Escape from supercooling with or without bubbles: gravitational wave signatures

Quasi-conformal models are an appealing scenario that can offer naturally a strongly supercooled phase transition and a period of thermal inflation in the early Universe. A crucial aspect for the viability of these models is how the Universe escapes from the supercooled state. One possibility is that thermal inflation phase ends by nucleation and percolation of true vacuum bubbles. This route is not, however, always efficient. In such case another escape mechanism, based on the growth of quantum fluctuations of the scalar field that eventually destabilize the false vacuum, becomes relevant. We study both of these cases in detail in a simple yet representative model. We determine the duration of the thermal inflation, the curvature power spectrum generated for the scales that exit horizon during the thermal inflation, and the stochastic gravitational wave background from the phase transition. We show that these gravitational waves provide an observable signal from the thermal inflation in almost the entire parameter space of interest. Furthermore, the shape of the gravitational wave spectrum can be used to ascertain how the Universe escaped from supercooling.