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Register a new userBlack holes and up-tunneling suppress Boltzmann brains
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Eternally inflating universes lead to an infinite number of Boltzmann brains but also an infinite number of ordinary observers. If we use the scale factor measure to regularize these infinities, the ordinary observers dominate the Boltzmann brains if the vacuum decay rate of each vacuum is larger than its Boltzmann brain nucleation rate. Here we point out that nucleation of small black holes should be counted in the vacuum decay rate, and this rate is always larger than the Boltzmann brain rate, if the minimum Boltzmann brain mass is more than the Planck mass. We also discuss nucleation of small, rapidly inflating regions, which may also have a higher rate than Boltzmann brains. This process also affects the distribution of the different vacua in eternal inflation.
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Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang. A theory in which most observers are of the Boltzmann Brain type is generally thought to be unacceptable, although opinions differ. I argue that such theories are indeed unacceptable: the real problem is with fluctuations into observers who are locally identical to ordinary observers, and their existence cannot be swept under the rug by a choice of probability distributions over observers. The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed.
To make predictions for an eternally inflating multiverse, one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes cooling from hot big bang conditions - must not be vastly outnumbered by Boltzmann brains - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.
Many modern cosmological scenarios feature large volumes of spacetime in a de Sitter vacuum phase. Such models are said to be faced with a Boltzmann Brain problem - the overwhelming majority of observers with fixed local conditions are random fluctuations in the de Sitter vacuum, rather than arising via thermodynamically sensible evolution from a low-entropy past. We argue that this worry can be straightforwardly avoided in the Many-Worlds (Everett) approach to quantum mechanics, as long as the underlying Hilbert space is infinite-dimensional. In that case, de Sitter settles into a truly stationary quantum vacuum state. While there would be a nonzero probability for observing Boltzmann-Brain-like fluctuations in such a state, observation refers to a specific kind of dynamical process that does not occur in the vacuum (which is, after all, time-independent). Observers are necessarily out-of-equilibrium physical systems, which are absent in the vacuum. Hence, the fact that projection operators corresponding to states with observers in them do not annihilate the vacuum does not imply that such observers actually come into existence. The Boltzmann Brain problem is therefore much less generic than has been supposed.
The standard $Lambda$CDM model provides an excellent fit to current cosmological observations but suffers from a potentially serious Boltzmann Brain problem. If the universe enters a de Sitter vacuum phase that is truly eternal, there will be a finite temperature in empty space and corresponding thermal fluctuations. Among these fluctuations will be intelligent observers, as well as configurations that reproduce any local region of the current universe to arbitrary precision. We discuss the possibility that the escape from this unacceptable situation may be found in known physics: vacuum instability induced by the Higgs field. Avoiding Boltzmann Brains in a measure-independent way requires a decay timescale of order the current age of the universe, which can be achieved if the top quark pole mass is approximately 178 GeV. Otherwise we must invoke new physics or a particular cosmological measure before we can consider $Lambda$CDM to be an empirical success.
We derive the quadratic action for the physical degrees of freedom of massless spin-0, spin-1, and spin-2 perturbations on a Schwarzschild--(A)dS background in arbitrary dimensions. We then use these results to compute the static response of asymptotically flat Schwarzschild black holes to external fields. Our analysis reproduces known facts about black hole Love numbers, in particular that they vanish for all types of perturbation in four spacetime dimensions, but also leads to new results. For instance, we find that neutral Schwarzschild black holes polarize in the presence of an electromagnetic background in any number of spacetime dimensions except four. Moreover, we calculate for the first time black hole Love numbers for vector-type gravitational perturbations in higher dimensions and find that they generically do not vanish. Along the way, we shed some light on an apparent discrepancy between previous results in the literature, and clarify some aspects of the matching between perturbative calculations of static response on a Schwarzschild background and the point-particle effective theory
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