Phenomenology of the CAH+ measure

The CAH+ measure regulates the infinite spacetime volume of the multiverse by constructing a surface of constant comoving apparent horizon (CAH) and then removing the future lightcones of all points on that surface (the latter prescription is referred to by the "+" in the name of the measure). This measure was motivated by the conjectured duality between the bulk of the multiverse and its future infinity and by the causality condition, requiring that the cutoff surfaces of the measure should be spacelike or null. Here we investigate the phenomenology of the CAH+ measure and find that it does not suffer from any known pathologies. The distribution for the cosmological constant Lambda derived from this measure is in a good agreement with the observed value, and the distribution for the number of inflationary e-foldings satisfies the observational constraint. The CAH+ measure does not exhibit any "runaway" behaviors at zero or negative values of Lambda, which have been recently shown to afflict a number of other measures.Comment: 35 pages, including 6 figures and 2 appendices; v2 corrections in Section 2.4, conclusions unchange

Statistical Understanding of Quark and Lepton Masses in Gaussian Landscapes

The fundamental theory of nature may allow a large landscape of vacua. Even if the theory contains a unified gauge symmetry, the 22 flavor parameters of the Standard Model, including neutrino masses, may be largely determined by the statistics of this landscape, and not by any symmetry. Then the measured values of the flavor parameters do not lead to any fundamental symmetries, but are statistical accidents; their precise values do not provide any insights into the fundamental theory, rather the overall pattern of flavor reflects the underlying landscape. We investigate whether random selection from the statistics of a simple landscape can explain the broad patterns of quark, charged lepton, and neutrino masses and mixings. We propose Gaussian landscapes as simplified models of landscapes where Yukawa couplings result from overlap integrals of zero-mode wavefunctions in higher-dimensional supersymmetric gauge theories. In terms of just five free parameters, such landscapes can account for all gross features of flavor, including: the hierarchy of quark and charged lepton masses; small quark mixing angles, with 13 mixing less than 12 and 23 mixing; very light Majorana neutrino masses, with the solar to atmospheric neutrino mass ratio consistent with data; distributions for leptonic 12 and 23 mixings that are peaked at large values, while the distribution for 13 mixing is peaked at low values; and order unity CP violating phases in both the quark and lepton sectors. While the statistical distributions for flavor parameters are broad, the distributions are robust to changes in the geometry of the extra dimensions. Constraining the distributions by loose cuts about observed values leads to narrower distributions for neutrino measurements of 13 mixing, CP violation, and neutrinoless double beta decay.Comment: 86 pages, 26 figures, 2 tables, and table of content

Quark and Lepton Masses from Gaussian Landscapes

The flavor structure of the standard model (SM) might arise from random selection on a landscape. We propose a class of simple models, “Gaussian landscapes,” where Yukawa couplings derive from overlap integrals of Gaussian wave functions on extra-dimensions. Statistics of vacua are generated by scanning the peak positions of these zero-modes, giving probability distributions for all flavor observables. Gaussian landscapes can account for all observed flavor patterns with few free parameters. Although they give broad probability distributions, the predictions are correlated and accounting for measured parameters sharpens the distributions of future neutrino measurements

Neutrino mixing and mass hierarchy in Gaussian landscapes

The flavor structure of the Standard Model may arise from random selection on a landscape. In a class of simple models, called "Gaussian landscapes," Yukawa couplings derive from overlap integrals of Gaussian zero-mode wavefunctions on an extra-dimensional space. Statistics of vacua are generated by scanning the peak positions of these wavefunctions, giving probability distributions for all flavor observables. Gaussian landscapes can account for all of the major features of flavor, including both the small electroweak mixing in the quark sector and the large mixing observed in the lepton sector. We find that large lepton mixing stems directly from lepton doublets having broad wavefunctions on the internal manifold. Assuming the seesaw mechanism, we find the mass hierarchy among neutrinos is sensitive to the number of right-handed neutrinos, and can provide a good fit to neutrino oscillation measurements.Comment: 11 pages, 2 figure

A signature of anisotropic bubble collisions

Our universe may have formed via bubble nucleation in an eternally-inflating background. Furthermore, the background may have a compact dimension---the modulus of which tunnels out of a metastable minimum during bubble nucleation---which subsequently grows to become one of our three large spatial dimensions. When in this scenario our bubble universe collides with other ones like it, the collision geometry is constrained by the reduced symmetry of the tunneling instanton. While the regions affected by such bubble collisions still appear (to leading order) as disks in an observer's sky, the centers of these disks all lie on a single great circle, providing a distinct signature of anisotropic bubble nucleation.Comment: 10 pages, 5 figures; v2: crucial error corrected, conclusions revise

The scale of gravity and the cosmological constant within a landscape

It is possible that the scale of gravity, parameterized by the apparent Planck mass, may obtain different values within different universes in an encompassing multiverse. We investigate the range over which the Planck mass may scan while still satisfying anthropic constraints. The window for anthropically allowed values of the Planck mass may have important consequences for landscape predictions. For example, if the likelihood to observe some value of the Planck mass is weighted by the inflationary expansion factors of the universes that contain that value, then it appears extremely unlikely to observe the value of the Planck mass that is measured within our universe. This is another example of the runaway inflation problem discussed in recent literature. We also show that the window for the Planck mass significantly weakens the anthropic constraint upon the cosmological constant when both are allowed to vary over a landscape.Comment: 25 pages, 3 figures; v2: corrected minor computational errors in Sect. IV; v3: references added, version accepted by PR