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Depressions at the surface of an elastic spherical shell submitted to external pressure
Elasticity theory calculations predict the number N of depressions that
appear at the surface of a spherical thin shell submitted to an external
isotropic pressure. In a model that mainly considers curvature deformations, we
show that N only depends on the relative volume variation. Equilibrium
configurations show single depression (N=1) for small volume variations, then N
increases up to 6, before decreasing more abruptly due to steric constraints,
down to N=1 again for maximal volume variations. These predictions are
consistent with previously published experimental observations
Figures of merit for present and future dark energy probes
We compare current and forecasted constraints on dynamical dark energy models
from Type Ia supernovae and the cosmic microwave background using figures of
merit based on the volume of the allowed dark energy parameter space. For a
two-parameter dark energy equation of state that varies linearly with the scale
factor, and assuming a flat universe, the area of the error ellipse can be
reduced by a factor of ~10 relative to current constraints by future
space-based supernova data and CMB measurements from the Planck satellite. If
the dark energy equation of state is described by a more general basis of
principal components, the expected improvement in volume-based figures of merit
is much greater. While the forecasted precision for any single parameter is
only a factor of 2-5 smaller than current uncertainties, the constraints on
dark energy models bounded by -1<w<1 improve for approximately 6 independent
dark energy parameters resulting in a reduction of the total allowed volume of
principal component parameter space by a factor of ~100. Typical quintessence
models can be adequately described by just 2-3 of these parameters even given
the precision of future data, leading to a more modest but still significant
improvement. In addition to advances in supernova and CMB data, percent-level
measurement of absolute distance and/or the expansion rate is required to
ensure that dark energy constraints remain robust to variations in spatial
curvature.Comment: 9 pages, 7 figures; submitted to Phys. Rev.
Improved Constraints on The Neutral Intergalactic Hydrogen Surrounding Quasars at Redshifts z>6
We analyze the evolution of HII regions around the seven known SDSS quasars
at z>6. The comparison between observed and model radii of the HII regions
generated by these quasars individually, suggests that the surrounding
intergalactic hydrogen is significantly neutral. When all constraints are
combined, the existing quasar sample implies a volume averaged neutral fraction
that is larger than 10% at z>6. This limited sample permits a preliminary
analysis of the correlations between the quasar parameters, the sizes of their
HII regions, and the associated constraints on the neutral hydrogen fraction.
We find no evidence in these correlations to contradict the interpretation that
the red side of the Gunn-Peterson trough corresponds to the boundary between an
HII region and a partially neutral IGM.Comment: 9 pages, 4 figures. Submitted to Ap
Impact of Systematic Errors in Sunyaev-Zel'dovich Surveys of Galaxy Clusters
Future high-resolution microwave background measurements hold the promise of
detecting galaxy clusters throughout our Hubble volume through their
Sunyaev-Zel'dovich (SZ) signature, down to a given limiting flux. The number
density of galaxy clusters is highly sensitive to cluster mass through
fluctuations in the matter power spectrum, as well as redshift through the
comoving volume and the growth factor. This sensitivity in principle allows
tight constraints on such quantities as the equation of state of dark energy
and the neutrino mass. We evaluate the ability of future cluster surveys to
measure these quantities simultaneously when combined with PLANCK-like CMB
data. Using a simple effective model for uncertainties in the cluster mass-SZ
flux relation, we evaluate systematic shifts in cosmological constraints from
cluster SZ surveys. We find that a systematic bias of 10% in cluster mass
measurements can give rise to shifts in cosmological parameter estimates at
levels larger than the statistical errors. Systematic errors are
unlikely to be detected from the mass and redshift dependence of cluster number
counts alone; increasing survey size has only a marginal effect. Implications
for upcoming experiments are discussed.Comment: 12 pages, 6 figures; accepted to JCAP; revised to match submitted
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