463 research outputs found
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
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
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
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
The distribution of Omega_k from the scale-factor cutoff measure
Our universe may be contained in one among a diverging number of bubbles that
nucleate within an eternally inflating multiverse. A promising measure to
regulate the diverging spacetime volume of such a multiverse is the
scale-factor cutoff, one feature of which is bubbles are not rewarded for
having a longer duration of slow-roll inflation. Thus, depending on the
landscape distribution of the number of e-folds of inflation among bubbles like
ours, we might hope to measure spacetime curvature. We study a recently
proposed cartoon model of inflation in the landscape and find a reasonable
chance (about ten percent) that the curvature in our universe is well above the
value expected from cosmic variance. Anthropic selection does not strongly
select for curvature as small as is observed (relative somewhat larger values),
meaning the observational bound on curvature can be used to rule out landscape
models that typically give too little inflation.Comment: 14 pages, 7 figure
Negative vacuum energy densities and the causal diamond measure
Arguably a major success of the landscape picture is the prediction of a
small, non-zero vacuum energy density. The details of this prediction depends
in part on how the diverging spacetime volume of the multiverse is regulated, a
question that remains unresolved. One proposal, the causal diamond measure, has
demonstrated many phenomenological successes, including predicting a
distribution of positive vacuum energy densities in good agreement with
observation. In the string landscape, however, the vacuum energy density is
expected to take positive and negative values. We find the causal diamond
measure gives a poor fit to observation in such a landscape -- in particular,
99.6% of observers in galaxies seemingly just like ours measure a vacuum energy
density smaller than we do, most of them measuring it to be negative.Comment: 9 pages, 3 figures; v2: minor error fixed (results essentially
unchanged), reference added; v3: published version, includes a few
clarification
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