One of the surprises that the LHC had in stock for us is that the Higgs turned out to be slightly heavier than expected, which has consequences for the structure of our vacuum. The Higgs field fills the vacuum and gives particles their mass, and this Higgs-filled vacuum was thought to be the stable minimum of the Higgs’ potential. If the Higgs is sufficiently heavy though, and this is what current data indicates, then the potential has another minimum at energies lower than the present-day vacuum. This means that the vacuum which surrounds us today is a “false vacuum” and is only metastable, not perfectly, eternally stable. Our false vacuum will eventually decay into the lower energy state that is the “true vacuum,” and when this decay occurs, it will release an enormous amount of energy and tear apart all the currently-bound-together particles of matter.
On the list of events that deserve to be called End Of The World, “vacuum decay” comes in right after “big crunch,” closely followed by “gmail outage.”
From the measured Higgs mass and other parameters determining the potential, one can calculate how long it would take for our vacuum to decay. The false vacuum decays by locally tunneling into the true vacuum, first creating a bubble that then rapidly expands and takes over the whole universe. When the Higgs symmetry was initially broken, something very similar took place, possibly giving rise to the dominance of matter over antimatter in our Universe.
From our present Universe, the time it takes for the tunneling to happen depends on the height of the potential wall between the true vacuum and the false vacuum we’re currently in. Estimates show that for what we presently know about the decay time, it must be at least many orders of magnitude longer than the present age of the universe. And so, even if the vacuum eventually decays, this would happen long after stars have run out of fuel and life in our Universe has become impossible anyway. So, as long as gmail is up, there’s nothing to worry about.
Or so we thought.
In a recent paper out last week, Vacuum metastability with black holes, a group of researchers from the UK and Canada pointed out that this estimate for the vacuum decay rate does not take into account that gravitational fields can serve as nucleation seeds for vacuum decay, and thereby vastly increase the instability of the present vacuum. In their paper, Burda, Gregory and Moss calculated the probability of the false vacuum to tunnel into the true vacuum in the vicinity of black holes, and they find it to be hugely amplified relative to the tunneling probability in the absence of black holes. Using some sets of parameters for the Higgs potential compatible with existing data, they estimate the decay time to be roughly comparable to the time it takes a black hole to decay via Hawking radiation.
The dominant tunneling process that can happen nearby the black hole depends on the black hole’s mass. Large black holes have a very small curvature at the horizon, and so the tunnel probability is small and the Hawking temperature is very low. As the black hole loses mass due to evaporation, the temperature increases and so does the tunneling probability. At large masses the most likely state that the false vacuum tunnels to is a true vacuum with a black hole of smaller mass left inside. If the mass of the black hole is sufficiently small though, the most likely endstate of the tunneling process becomes simply a true vacuum bubble. In either case though, the true vacuum would start to rapidly expand.
This is to say, where the vacuum decay rate is larger than the Hawking radiation rate, the vacuum can become unstable near the edge of the black hole — and expand outward incredibly quickly — when a black hole is close to completely evaporating. Where Γ_D/Γ_H is bigger than one, that’s where the catastrophe is most likely to begin.
How long does it take for a black hole to evaporate down so that it is small enough to trigger the vacuum decay? That depends on the initial mass of the black hole. The larger the black hole, the longer it takes. All the black holes that we have observational evidence for — solar mass black holes and super-massive black holes — are so heavy they don’t presently evaporate at all because their temperature is below the temperature of the cosmic microwave background. They don’t lose mass, instead they grow.
However, it has been speculated that small black holes might have formed in the very early universe from large density fluctuations. These black holes are referred to as “primordial” black holes and could have pretty much any mass today. If they are around, some of them could have already evaporated or they could evaporate right now. Signatures for these black hole evaporation events have been looked for but nothing has been seen, though it has been speculated that some short-period γ-ray bursts might originate from such events.
If the calculations in the new paper are correct, we could now conclude that no black holes can have previously completely evaporated anywhere in our universe, because otherwise we wouldn’t be here anymore. Since the distribution of primordial black hole masses is not known, however, some of them could be around and come into the final phase of evaporation any time, spelling the end of the world as we know it.
Sounds pretty bad, I know. So to help you sleep better, here is the fine print.
First, primordial black holes, while not strictly speaking ruled out, are considered highly speculative among most cosmologists. The reason is that it is hard to find a model in which they are produced that doesn’t wind up creating way too many of them. You have to not only create a primordial black hole, you need to also be consistent with the Universe we’ve already observed. In order to form one, you need the Universe to be born with a density fluctuation that’s about 68% denser than average, whereas the primordial fluctuations we observe are about 0.003% denser than average. More importantly though, the parameters of the Higgs potential that go into the vacuum decay rate are based on the assumption that the standard model is the complete theory up to the scale where quantum gravity becomes relevant. But it is highly questionable that this is the case. In fact, it is widely believed to not be the case.
Oh, yes, and what about those tiny black holes at the LHC that were meant to eat up the planet in 2008? There is absolutely no indication that the LHC has produced even a single one of them, and at this point the idea seems very unlikely to be correct, but this too has not strictly speaking been ruled out. Could these LHC black holes also seed a vacuum decay?
This cannot be said based on the existing calculations in the Burda et al. paper. Not only because these LHC black holes would be higher dimensional, but also because the vacuum would then be higher dimensional, thus the whole theory is very different. It seems extremely unlikely that the mini black holes, even if they were produced at the LHC, could be harmful, for the same reasons that has previously been called upon: The LHC operates in an energy regime in which astrophysical collisions take place all the time. It doesn’t create events that are unprecedented in the history of the universe. In fact, if the Burda et al. calculation can be extended to higher dimensions, one can probably use it to rule out the idea of mini black holes at LHC energies altogether.
So as a theoretical physicist, this new result doesn’t make me worry about the end of the world, but instead I see it as a new way to obtain knowledge about the parameters in the standard model. The recent paper only laid out the calculation and showed results for some representative values, but I have been told that an upcoming work will present a more complete scan of the parameter space. This has the potential to develop into a very fruitful connection between cosmology, astrophysics, and collider experiments we can perform right here on Earth.
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