34 research outputs found
Energy conditions for a generally coupled scalar field outside a reflecting sphere
We calculate the stress-energy tensor for a scalar field with general
curvature coupling, outside a perfectly reflecting sphere with Dirichlet
boundary conditions. For conformal coupling we find that the null energy
condition is always obeyed, and therefore the averaged null energy condition
(ANEC) is also obeyed. Since the ANEC is independent of curvature coupling, we
conclude that the ANEC is obeyed for scalar fields with any curvature coupling
in this situation. We also show how the spherical case goes over to that of a
flat plate as one approaches the sphere.Comment: Accepted for publication in Phys. Rev.
Anthropic prediction in a large toy landscape
The successful anthropic prediction of the cosmological constant depends
crucially on the assumption of a flat prior distribution. However, previous
calculations in simplified landscape models showed that the prior distribution
is staggered, suggesting a conflict with anthropic predictions. Here we
analytically calculate the full distribution, including the prior and anthropic
selection effects, in a toy landscape model with a realistic number of vacua,
. We show that it is possible for the fractal prior
distribution we find to behave as an effectively flat distribution in a wide
class of landscapes, depending on the regime of parameter space. Whether or not
this possibility is realized depends on presently unknown details of the
landscape.Comment: 13 page
Energy conditions outside a dielectric ball
We show analytically that the vacuum electromagnetic stress-energy tensor
outside a ball with constant dielectric constant and permeability always obeys
the weak, null, dominant, and strong energy conditions. There are still no
known examples in quantum field theory in which the averaged null energy
condition in flat spacetime is violated.Comment: 12 pages, RevTex
Volume Weighted Measures of Eternal Inflation in the Bousso-Polchinski Landscape
We consider the cosmological dynamics associated with volume weighted
measures of eternal inflation, in the Bousso-Polchinski model of the string
theory landscape. We find that this measure predicts that observers are most
likely to find themselves in low energy vacua with one flux considerably larger
than the rest. Furthermore, it allows for a satisfactory anthropic explanation
of the cosmological constant problem by producing a smooth, and approximately
constant, distribution of potentially observable values of Lambda. The low
energy vacua selected by this measure are often short lived. If we require
anthropically acceptable vacua to have a minimum life-time of 10 billion years,
then for reasonable parameters a typical observer should expect their vacuum to
have a life-time of approximately 12 billion years. This prediction is model
dependent, but may point toward a solution to the coincidence problem of
cosmology.Comment: 35 pages, 8 figure
Probabilities in the inflationary multiverse
Inflationary cosmology leads to the picture of a "multiverse," involving an
infinite number of (spatially infinite) post-inflationary thermalized regions,
called pocket universes. In the context of theories with many vacua, such as
the landscape of string theory, the effective constants of Nature are
randomized by quantum processes during inflation. We discuss an analytic
estimate for the volume distribution of the constants within each pocket
universe. This is based on the conjecture that the field distribution is
approximately ergodic in the diffusion regime, when the dynamics of the fields
is dominated by quantum fluctuations (rather than by the classical drift). We
then propose a method for determining the relative abundances of different
types of pocket universes. Both ingredients are combined into an expression for
the distribution of the constants in pocket universes of all types.Comment: 18 pages, RevTeX 4, 2 figures. Discussion of the full probability in
Sec.VI is sharpened; the conclusions are strengthened. Note added explaining
the relation to recent work by Easther, Lim and Martin. Some references adde
Anthropic prediction for a large multi-jump landscape
The assumption of a flat prior distribution plays a critical role in the
anthropic prediction of the cosmological constant. In a previous paper we
analytically calculated the distribution for the cosmological constant,
including the prior and anthropic selection effects, in a large toy
``single-jump'' landscape model. We showed that it is possible for the fractal
prior distribution we found to behave as an effectively flat distribution in a
wide class of landscapes, but only if the single jump size is large enough. We
extend this work here by investigating a large () toy
``multi-jump'' landscape model. The jump sizes range over three orders of
magnitude and an overall free parameter determines the absolute size of the
jumps. We will show that for ``large'' the distribution of probabilities of
vacua in the anthropic range is effectively flat, and thus the successful
anthropic prediction is validated. However, we argue that for small , the
distribution may not be smooth.Comment: 33 pages, 7 figures Minor revisions made and references added. arXiv
admin note: substantial text overlap with arXiv:0705.256
Measures for a Transdimensional Multiverse
The multiverse/landscape paradigm that has emerged from eternal inflation and
string theory, describes a large-scale multiverse populated by "pocket
universes" which come in a huge variety of different types, including different
dimensionalities. In order to make predictions in the multiverse, we need a
probability measure. In landscapes, the scale factor cutoff measure
has been previously shown to have a number of attractive properties. Here we
consider possible generalizations of this measure to a transdimensional
multiverse. We find that a straightforward extension of scale factor cutoff to
the transdimensional case gives a measure that strongly disfavors large amounts
of slow-roll inflation and predicts low values for the density parameter
, in conflict with observations. A suitable generalization, which
retains all the good properties of the original measure, is the "volume factor"
cutoff, which regularizes the infinite spacetime volume using cutoff surfaces
of constant volume expansion factor.Comment: 30 pages, 1 figure Minor revisions, reference adde
Dynamical compactification from de Sitter space
We show that D-dimensional de Sitter space is unstable to the nucleation of
non-singular geometries containing spacetime regions with different numbers of
macroscopic dimensions, leading to a dynamical mechanism of compactification.
These and other solutions to Einstein gravity with flux and a cosmological
constant are constructed by performing a dimensional reduction under the
assumption of q-dimensional spherical symmetry in the full D-dimensional
geometry. In addition to the familiar black holes, black branes, and
compactification solutions we identify a number of new geometries, some of
which are completely non-singular. The dynamical compactification mechanism
populates lower-dimensional vacua very differently from false vacuum eternal
inflation, which occurs entirely within the context of four-dimensions. We
outline the phenomenology of the nucleation rates, finding that the
dimensionality of the vacuum plays a key role and that among vacua of the same
dimensionality, the rate is highest for smaller values of the cosmological
constant. We consider the cosmological constant problem and propose a novel
model of slow-roll inflation that is triggered by the compactification process.Comment: Revtex. 41 pages with 24 embedded figures. Minor corrections and
added reference
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