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Register a new userRegulating Eternal Inflation
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We present an interpretation of the physics of space-times undergoing eternal inflation by repeated nucleation of bubbles. In many cases the physics can be interpreted in terms of the quantum mechanics of a system with a finite number of states. If this interpretation is correct, the conventional picture of these space-times is misleading.
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In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that we live at asymptotic late times, when the occupational probabilities of vacua has settled to a near-equilibrium distribution. In this paper we further develop the idea that we instead exist during the approach to equilibrium, much earlier than the exponentially-long mixing time. In this case we are most likely to reside in vacua that are easily accessed dynamically. Using first-passage statistics, we prove that vacua that maximize their space-time volume at early times have: 1. maximal ever-hitting probability; 2. minimal mean first-passage time; and 3. minimal decay rate. These requirements are succinctly captured by an early-time measure. The idea that we live at early times is a predictive guiding principle, with many phenomenological implications. First, our vacuum should lie deep in a funneled region, akin to folding energy landscapes of proteins. Second, optimal landscape regions are characterized by relatively short-lived vacua, with lifetime of order the de Sitter Page time. For our vacuum, this lifetime is $sim 10^{130}$~years, which is consistent with the Standard Model estimate due to Higgs metastability. Third, the measure favors vacua with small, positive vacuum energy. This can address the cosmological constant problem, provided there are sufficiently many vacua in the entire ensemble of funnels. As a concrete example, we study the Bousso-Polchinski lattice of flux vacua, and find that the early-time measure favors lattices with the fewest number of flux dimensions. This favors compactifications with a large hierarchy between the lightest modulus and all other Kahler and complex structure moduli.
We model the essential features of eternal inflation on the landscape of a dense discretuum of vacua by the potential $V(phi)=V_{0}+delta V(phi)$, where $|delta V(phi)|ll V_{0}$ is random. We find that the diffusion of the distribution function $rho(phi,t)$ of the inflaton expectation value in different Hubble patches may be suppressed due to the effect analogous to the Anderson localization in disordered quantum systems. At $t to infty$ only the localized part of the distribution function $rho (phi, t)$ survives which leads to dynamical selection principle on the landscape. The probability to measure any but a small value of the cosmological constant in a given Hubble patch on the landscape is exponentially suppressed at $tto infty$.
An eternally inflating universe produces an infinite amount of spatial volume, so every possible event happens an infinite number of times, and it is impossible to define probabilities in terms of frequencies. This problem is usually addressed by means of a measure, which regulates the infinities and produces meaningful predictions. I argue that any measure should obey certain general axioms, but then give a simple toy model in which one can prove that no measure obeying the axioms exists. In certain cases of eternal inflation there are measures that obey the axioms, but all such measures appear to be unacceptable for other reasons. Thus the problem of defining sensible probabilities in eternal inflation seems not be solved.
The much-discussed swampland conjectures suggest significant constraints on the properties of string theory landscape and on the nature of the multiverse that this landscape can support. The conjectures are especially constraining for models of inflation; in particular, they exclude the existence of de Sitter (dS) vacua. If the conjectures are false and dS vacua do exist, it still appears that their construction in string theory requires a fair amount of fine-tuning, so they may be vastly outnumbered by AdS vacua. Here we explore the multiverse structure suggested by these considerations. We consider two scenarios: (i) a landscape where dS vacua are rare and (ii) a landscape where dS vacua do not exist and the dS potential maxima and saddle points are not flat enough to allow for the usual hilltop inflation, even though slow-roll inflation is possible on the slopes of the potential. We argue that in both scenarios inflation is eternal and all parts of the landscape that can support inflation get represented in the multiverse. The spacetime structure of the multiverse in such models is nontrivial and is rather different from the standard picture.
Current data from the Planck satellite and the BICEP2 telescope favor, at around the $2 sigma$ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running $alpha < 0$, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on $n_{rm S}$ from Planck, this corresponds to an upper bound of the running $alpha < - 4 times 10^{-5}$, so that even tiny running of the scalar spectral index is sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In single-field inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as $10^4$ e-folds.
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