94 research outputs found
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
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, 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
A Framework for the Landscape
It seems likely that string theory has a landscape of vacua that includes
very many metastable de Sitter spaces. However, as emphasized by Banks, Dine
and Gorbatov, no current framework exists for examining these metastable vacua
in string theory. In this paper we attempt to correct this situation by
introducing an eternally inflating background in which the entire collection of
accelerating cosmologies is present as intermediate states. The background is a
classical solution which consists of a bubble of zero cosmological constant
inside de Sitter space, separated by a domain wall. At early and late times the
flat space region becomes infinitely big, so an S-matrix can be defined.
Quantum mechanically, the system can tunnel to an intermediate state which is
pure de Sitter space. We present evidence that a string theory S-matrix makes
sense in this background and contains metastable de Sitter space as an
intermediate state.Comment: 29+13 pages, 25 figures; v2: minor corrections, references adde
Anthropic reasoning in multiverse cosmology and string theory
Anthropic arguments in multiverse cosmology and string theory rely on the
weak anthropic principle (WAP). We show that the principle, though ultimately a
tautology, is nevertheless ambiguous. It can be reformulated in one of two
unambiguous ways, which we refer to as WAP_1 and WAP_2. We show that WAP_2, the
version most commonly used in anthropic reasoning, makes no physical
predictions unless supplemented by a further assumption of "typicality", and we
argue that this assumption is both misguided and unjustified. WAP_1, however,
requires no such supplementation; it directly implies that any theory that
assigns a non-zero probability to our universe predicts that we will observe
our universe with probability one. We argue, therefore, that WAP_1 is
preferable, and note that it has the benefit of avoiding the inductive
overreach characteristic of much anthropic reasoning.Comment: 7 pages. Expanded discussion of selection effects and some minor
clarifications, as publishe
Making predictions in the multiverse
I describe reasons to think we are living in an eternally inflating
multiverse where the observable "constants" of nature vary from place to place.
The major obstacle to making predictions in this context is that we must
regulate the infinities of eternal inflation. I review a number of proposed
regulators, or measures. Recent work has ruled out a number of measures by
showing that they conflict with observation, and focused attention on a few
proposals. Further, several different measures have been shown to be
equivalent. I describe some of the many nontrivial tests these measures will
face as we learn more from theory, experiment, and observation.Comment: 20 pages, 3 figures; invited review for Classical and Quantum
Gravity; v2: references improve
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
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
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
Exploring a string-like landscape
We explore inflationary trajectories within randomly-generated
two-dimensional potentials, considered as a toy model of the string landscape.
Both the background and perturbation equations are solved numerically, the
latter using the two-field formalism of Peterson and Tegmark which fully
incorporates the effect of isocurvature perturbations. Sufficient inflation is
a rare event, occurring for only roughly one in potentials. For models
generating sufficient inflation, we find that the majority of runs satisfy
current constraints from WMAP. The scalar spectral index is less than 1 in all
runs. The tensor-to-scalar ratio is below the current limit, while typically
large enough to be detected by next-generation CMB experiments and perhaps also
by Planck. In many cases the inflationary consistency equation is broken by the
effect of isocurvature modes.Comment: 24 pages with 8 figures incorporated, matches version accepted by
JCA
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