A Conformal Field Theory for Eternal Inflation

We study a statistical model defined by a conformally invariant distribution of overlapping spheres in arbitrary dimension d. The model arises as the asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space, and also as the asymptotic distribution of bubble collisions with the domain wall of a fiducial "observation bubble" in d+2 dimensional de Sitter space. In this note we calculate the 2-,3-, and 4-point correlation functions of exponentials of the "bubble number operator" analytically in d=2. We find that these correlators, when carefully defined, are free of infrared divergences, covariant under the global conformal group, charge conserving, and transform with positive conformal dimensions that are related in a novel way to the charge. Although by themselves these operators probably do not define a full-fledged conformal field theory, one can use the partition function on a sphere to compute an approximate central charge in the 2D case. The theory in any dimension has a noninteracting limit when the nucleation rate of the bubbles in the bulk is very large. The theory in two dimensions is related to some models of continuum percolation, but it is conformal for all values of the tunneling rate.Comment: 30 pages, 8 figure

Bubble collisions and measures of the multiverse

To compute the spectrum of bubble collisions seen by an observer in an eternally-inflating multiverse, one must choose a measure over the diverging spacetime volume, including choosing an "initial" hypersurface below which there are no bubble nucleations. Previous calculations focused on the case where the initial hypersurface is pushed arbitrarily deep into the past. Interestingly, the observed spectrum depends on the orientation of the initial hypersurface, however one's ability observe the effect rapidly decreases with the ratio of inflationary Hubble rates inside and outside one's bubble. We investigate whether this conclusion might be avoided under more general circumstances, in particular placing the observer's bubble near the initial hypersurface. We find that it is not. As a point of reference, a substantial appendix reviews relevant aspects of the measure problem of eternal inflation.Comment: 24 pages, two figures, plus 16-page appendix with one figure; v2: minor improvements and clarifications, conclusions unchanged (version to appear in JCAP

Holographic Multiverse

We explore the idea that the dynamics of the inflationary multiverse is encoded in its future boundary, where it is described by a lower dimensional theory which is conformally invariant in the UV. We propose that a measure for the multiverse, which is needed in order to extract quantitative probabilistic predictions, can be derived in terms of the boundary theory by imposing a UV cutoff. In the inflationary bulk, this is closely related (though not identical) to the so-called scale factor cutoff measure.Comment: 23 pages, 4 figures. Replaced to match published versio

Many worlds in one

A generic prediction of inflation is that the thermalized region we inhabit is spatially infinite. Thus, it contains an infinite number of regions of the same size as our observable universe, which we shall denote as \O-regions. We argue that the number of possible histories which may take place inside of an \O-region, from the time of recombination up to the present time, is finite. Hence, there are an infinite number of \O-regions with identical histories up to the present, but which need not be identical in the future. Moreover, all histories which are not forbidden by conservation laws will occur in a finite fraction of all \O-regions. The ensemble of \O-regions is reminiscent of the ensemble of universes in the many-world picture of quantum mechanics. An important difference, however, is that other \O-regions are unquestionably real.Comment: 9 pages, 2 figures, comments and references adde

Out of equilibrium: understanding cosmological evolution to lower-entropy states

Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate the spacetime structure of various fluctuations in (stable and metastable) de Sitter space and thermal anti-de Sitter space.Comment: 27 pages, 11 figure

The Capaciousness of No: Affective Refusals as Literacy Practices

© 2020 The Authors. Reading Research Quarterly published by Wiley Periodicals, Inc. on behalf of International Literacy Association The authors considered the capacious feeling that emerges from saying no to literacy practices, and the affective potential of saying no as a literacy practice. The authors highlight the affective possibilities of saying no to normative understandings of literacy, thinking with a series of vignettes in which children, young people, and teachers refused literacy practices in different ways. The authors use the term capacious to signal possibilities that are as yet unthought: a sense of broadening and opening out through enacting no. The authors examined how attention to affect ruptures humanist logics that inform normative approaches to literacy. Through attention to nonconscious, noncognitive, and transindividual bodily forces and capacities, affect deprivileges the human as the sole agent in an interaction, thus disrupting measurements of who counts as a literate subject and what counts as a literacy event. No is an affective moment. It can signal a pushback, an absence, or a silence. As a theoretical and methodological way of thinking/feeling with literacy, affect proposes problems rather than solutions, countering solution-focused research in which the resistance is to be overcome, co-opted, or solved. Affect operates as a crack or a chink, a tiny ripple, a barely perceivable gesture, that can persist and, in doing so, hold open the possibility for alternative futures

αs\alpha_s from τ\tau decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion

We consider the determination of $\alpha_s$ from $\tau$ hadronic decays, by investigating the contour-improved (CI) and the fixed-order (FO) renormalization group summations in the frame of a new perturbation expansion of QCD, which incorporates in a systematic way the available information about the divergent character of the series. The new expansion functions, which replace the powers of the coupling, are defined by the analytic continuation in the Borel complex plane, achieved through an optimal conformal mapping. Using a physical model recently discussed by Beneke and Jamin, we show that the new CIPT approaches the true results with great precision when the perturbative order is increased, while the new FOPT gives a less accurate description in the regions where the imaginary logarithms present in the expansion of the running coupling are large. With the new expansions, the discrepancy of 0.024 in $\alpha_s(m_\tau^2)$ between the standard CI and FO summations is reduced to only 0.009. From the new CIPT we predict $\alpha_s(m_\tau^2)= 0.320 ^{+0.011}_{-0.009}$, which practically coincides with the result of the standard FOPT, but has a more solid theoretical basis