Bubble, Bubble, Flow and Hubble: Large Scale Galaxy Flow from Cosmological Bubble Collisions

We study large scale structure in the cosmology of Coleman-de Luccia bubble collisions. Within a set of controlled approximations we calculate the effects on galaxy motion seen from inside a bubble which has undergone such a collision. We find that generically bubble collisions lead to a coherent bulk flow of galaxies on some part of our sky, the details of which depend on the initial conditions of the collision and redshift to the galaxy in question. With other parameters held fixed the effects weaken as the amount of inflation inside our bubble grows, but can produce measurable flows past the number of efolds required to solve the flatness and horizon problems.Comment: 30 pages, 8 figures, pdftex, minor corrections and references adde

Anthropic Explanation of the Dark Matter Abundance

I use Bousso's causal diamond measure to make a statistical prediction for the dark matter abundance, assuming an axion with a large decay constant f_a >> 10^{12} GeV. Using a crude approximation for observer formation, the prediction agrees well with observation: 30% of observers form in regions with less dark matter than we observe, while 70% of observers form in regions with more dark matter. Large values of the dark matter ratio are disfavored by an elementary effect: increasing the amount of dark matter while holding fixed the baryon to photon ratio decreases the number of baryons inside one horizon volume. Thus the prediction is rather insensitive to assumptions about observer formation in universes with much more dark matter than our own. The key assumption is that the number of observers per baryon is roughly independent of the dark matter ratio for ratios near the observed value.Comment: 10 pages; v3: published version, references adde

Polarizing Bubble Collisions

We predict the polarization of cosmic microwave background (CMB) photons that results from a cosmic bubble collision. The polarization is purely E-mode, symmetric around the axis pointing towards the collision bubble, and has several salient features in its radial dependence that can help distinguish it from a more conventional explanation for unusually cold or hot features in the CMB sky. The anomalous "cold spot" detected by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite is a candidate for a feature produced by such a collision, and the Planck satellite and other proposed surveys will measure the polarization on it in the near future. The detection of such a collision would provide compelling evidence for the string theory landscape.Comment: Published version. 15 pages, 8 figure

Spatial Curvature Falsifies Eternal Inflation

Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured within one Hubble volume receives contributions from long wavelength perturbations, and will not in general be zero. These same perturbations determine the Cosmic Microwave Background (CMB) temperature fluctuations, which are O(10^-5). Consequently, the low-l multipole moments in the CMB temperature map predict the value of the measured spatial curvature \Omega_k. On this basis we argue that a measurement of |\Omega_k| > 10^-4 would rule out slow-roll eternal inflation in our past with high confidence, while a measurement of \Omega_k < -10^-4 (which is positive curvature, a locally closed universe) rules out false-vacuum eternal inflation as well, at the same confidence level. In other words, negative curvature (a locally open universe) is consistent with false-vacuum eternal inflation but not with slow-roll eternal inflation, and positive curvature falsifies both. Near-future experiments will dramatically extend the sensitivity of \Omega_k measurements and constitute a sharp test of these predictions.Comment: 16+2 pages, 2 figure

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

Multi-field open inflation model and multi-field dynamics in tunneling

We consider a multi-field open inflation model, in which one of the fields dominates quantum tunneling from a false vacuum while the other field governs slow-roll inflation within the bubble nucleated from false vacuum decay. We call the former the tunneling field and the latter the inflaton field. In the limit of a negligible interaction between the two fields, the false vacuum decay is described by a Coleman-De Luccia instanton. Here we take into account the coupling between the two fields and construct explicitly a multi-field instanton for a simple quartic potential model. We also solve the evolution of the scalar fields within the bubble. We find our model realizes open inflation successfully. This is the first concrete, viable model of open inflation realized with a simple potential. We then study the effect of the multi-field dynamics on the false vacuum decay, specifically on the tunneling rate. We find the tunneling rate increases in general in comparison with the single field case, though the increase is small unless the inflaton affects the instanton solution substantially.Comment: 13 pages, 4 figure