It is well known that anthropic selection from a landscape with a flat prior distribution of cosmological constant Λ gives a reasonable fit to observation. However, a realistic model of the multiverse has a physical volume that diverges with time, and the predicted distribution of Λ depends on how the spacetime volume is regulated. We study a simple model of the multiverse with probabilities regulated by a scale-factor cutoff, and calculate the resulting distribution, considering both positive and negative values of Λ. The results are in good agreement with observation. In particular, the scalefactor cutoff strongly suppresses the probability for values of Λ that are more than about ten times the observed value. We also discuss several qualitative features of the scale-factor cutoff, including aspects of the distributions of the curvature parameter Ω and the primordial density contrast Q.

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.Comment: 32 pp, 2 figs. Modified to conform to the version accepted by Phys. Rev. D. The last paragraph of Sec. V-A, about Boltzmann brains in Minkowski space, has been significantly enlarged. Two sentences were added to the introduction concerning the classical approximation and the hope of finding a motivating principle for the measure. Several references were adde

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. Then the reduced symmetry of the background is equivalent to anisotropic initial conditions in our bubble universe. We compute the inflationary spectrum in such a scenario and, as a first step toward understanding the effects of anisotropy, project it onto spherical harmonics. The resulting spectrum exhibits anomalous multipole correlations, their relative amplitude set by the present curvature parameter, which appear to extend to arbitrarily large multipole moments. This raises the possibility of future detection, if slow-roll inflation does not last too long within our bubble. A full understanding of the observational signal must account for the effects of background anisotropy on photon free streaming, and is left to future work.

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.

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 wave functions 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 in the basis with quarks arranged according to mass, 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 mixings sin2 12 and sin2 23 that are peaked at large values, while the distribution for sin2 13 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 , CP violation, and neutrinoless double beta decay.

Recently a mechanism was proposed whereby the primordial density perturbations are generated at the end of inflation. We continue the analysis of the proposed model of this mechanism and calculate the maximum extent to which the density perturbations produced via this model can dominate over those of the standard inflationary paradigm. In addition, we provide a straightforward variation of this model which allows for greater amplification of the density perturbations. Finally, we show that a variation in the implementation of the original model results in significant non-Gaussianities in the resulting spectrum of density perturbations. The level of non-Gaussianities can be made to saturate the current observational bound.

It is possible that the scale of gravity, parametrized 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 on the cosmological constant when both are allowed to vary over a landscape.

We review the theoretical status of the predictions for the decay rate differences in the neutral B-system. We find (∆Γ/Γ) Bs = (12 ± 5) · 10 −2 and (∆Γ/Γ) B d = (3 ± 1.2) · 10 −3 .