232 research outputs found
The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
Several studies have proposed that the shape of the Universe may be a
Poincare dodecahedral space (PDS) rather than an infinite, simply connected,
flat space. Both models assume a close to flat FLRW metric of about 30% matter
density. We study two predictions of the PDS model. (i) For the correct model,
the spatial two-point cross-correlation function, \ximc, of temperature
fluctuations in the covering space, where the two points in any pair are on
different copies of the surface of last scattering (SLS), should be of a
similar order of magnitude to the auto-correlation function, \xisc, on a
single copy of the SLS. (ii) The optimal orientation and identified circle
radius for a "generalised" PDS model of arbitrary twist , found by
maximising \ximc relative to \xisc in the WMAP maps, should yield . We optimise the cross-correlation at scales < 4.0 h^-1 Gpc
using a Markov chain Monte Carlo (MCMC) method over orientation, circle size
and . Both predictions were satisfied: (i) an optimal "generalised" PDS
solution was found, with a strong cross-correlation between points which would
be distant and only weakly correlated according to the simply connected
hypothesis, for two different foreground-reduced versions of the WMAP 3-year
all-sky map, both with and without the kp2 Galaxy mask: the face centres are
\phi
\in [0,2\pi]$, is about 6-9%.Comment: 20 pages, 22 figures, accepted in Astronomy & Astrophysics, software
available at http://adjani.astro.umk.pl/GPLdownload/dodec/ and MCMCs at
http://adjani.astro.umk.pl/GPLdownload/MCM
Topology of the Universe: background and recent observational approaches
Is the Universe (a spatial section thereof) finite or infinite? Knowing the
global geometry of a Friedmann-Lema\^{\i}tre (FL) universe requires knowing
both its curvature and its topology. A flat or hyperbolic (``open'') FL
universe is {\em not} necessarily infinite in volume.
Multiply connected flat and hyperbolic models are, in general, as consistent
with present observations on scales of 1-20{\hGpc} as are the corresponding
simply connected flat and hyperbolic models. The methods of detecting multiply
connected models (MCM's) are presently in their pioneering phase of development
and the optimal observationally realistic strategy is probably yet to be
calculated. Constraints against MCM's on ~1-4 h^{-1} Gpc scales have been
claimed, but relate more to inconsistent assumptions on perturbation statistics
rather than just to topology. Candidate 3-manifolds based on hypothesised
multiply imaged objects are being offered for observational refutation.
The theoretical and observational sides of this rapidly developing subject
have yet to make any serious contact, but the prospects of a significant
detection in the coming decade may well propel the two together.Comment: 5 pages, proceedings of the Workshop ``Cosmology: Observations
Confront Theories,'' 11-17 Jan 1999, IIT Kharagpur, West Bengal, to appear in
Pramana - Journal of Physic
Characteristic Energy of the Coulomb Interactions and the Pileup of States
Tunneling data on crystals confirm
Coulomb interaction effects through the dependence of the
density of states. Importantly, the data and analysis at high energy, E, show a
pileup of states: most of the states removed from near the Fermi level are
found between ~40 and 130 meV, from which we infer the possibility of universal
behavior. The agreement of our tunneling data with recent photoemission results
further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR
Poincare dodecahedral space parameter estimates
We aim to improve the surface of last scattering (SLS) optimal
cross-correlation method in order to refine estimates of the Poincar\'e
dodecahedral space (PDS) cosmological parameters. We analytically derive the
formulae required to exclude points on the sky that cannot be members of close
SLS-SLS cross-pairs. These enable more efficient pair selection without
sacrificing uniformity of the underlying selection process. In certain cases
this decreases the calculation time and increases the number of pairs per
separation bin. (i) We recalculate Monte Carlo Markov Chains (MCMC) on the
five-year WMAP data; and (ii) we seek PDS solutions in a small number of
Gaussian random fluctuation (GRF) simulations. For 5 < alpha/deg < 60, a
calculation speed-up of 3-10 is obtained. (i) The best estimates of the PDS
parameters for the five-year WMAP data are similar to those for the three-year
data. (ii) Comparison of the optimal solutions found by the MCMC chains in the
observational map to those found in the simulated maps yields a slightly
stronger rejection of the simply connected model using than using the
twist angle . The best estimate of implies that_given a large
scale auto-correlation as weak as that observed,_ the PDS-like
cross-correlation signal in the WMAP data is expected with a probability of
less than about 10%. The expected distribution of from the GRF
simulations is approximately Gaussian around zero, it is not uniform on
. We infer that for an infinite, flat, cosmic concordance model
with Gaussian random fluctuations, the chance of finding_both_ (a) a large
scale auto-correlation as weak as that observed,_and_ (b) a PDS-like signal
similar to that observed is less than about 0.015% to 1.25%.Comment: 18 pages, 19 figures, accepted in Astronomy & Astrophysics, software
available at http://cosmo.torun.pl/GPLdownload/dodec/ and MCMCs at
http://cosmo.torun.pl/GPLdownload/MCMC/ ; v2: histograms added, several minor
changes, matches accepted versio
A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently
regained interest as a good fit to the observed cosmic microwave background
temperature fluctuations. However, it is generally thought that a globally,
exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a
probability space on the set F of compact, comoving, 3-spatial sections of FLRW
models, a physically motivated hypothesis is proposed, using the density
parameter Omega as a derived rather than fundamental parameter. We assume that
the processes that select the 3-manifold also select a global mass-energy and a
Hubble parameter. The inferred range in Omega consists of a single real value
for any 3-manifold. Thus, the obvious measure over F is the discrete measure.
Hence, if the global mass-energy and Hubble parameter are a function of
3-manifold choice among compact FLRW models, then probability spaces
parametrised by Omega do not, in general, give a zero probability of a flat
model. Alternatively, parametrisation by the injectivity radius r_inj ("size")
suggests the Lebesgue measure. In this case, the probability space over the
injectivity radius implies that flat models occur almost surely (a.s.), in the
sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3:
generalisation: m, H functions of
Determining the shape of the Universe using discrete sources
Suppose we have identified three clusters of galaxies as being topological
copies of the same object. How does this information constrain the possible
models for the shape of our Universe? It is shown here that, if the Universe
has flat spatial sections, these multiple images can be accommodated within any
of the six classes of compact orientable 3-dimensional flat space forms.
Moreover, the discovery of two more triples of multiple images in the
neighbourhood of the first one, would allow the determination of the topology
of the Universe, and in most cases the determination of its size.Comment: 11 pages, no figure
Europe's confused transmutation: the realignment of moral cartography in Juan de la Cosa's Mappa Mundi (1500)
Following the voyages of Christopher Columbus, John Cabot, Alonso de Ojeda and Amerigo Vespucci in the last decade of the fifteenth century, the New World of the Americas entered the cartographic and moral consciousness of Europe. In the 1500 mappa mundi of Juan de la Cosa, navigator and map-maker, we see Europe as a hybrid moral entity, a transitional blend of the medieval and the modern at the crossroads between two mappings of Europe. This paper argues that the Juan De la Cosa map represents a blurred transition between map-making traditions and a mixed moral rhetoric of European identity. The De la Cosa map operates across two sets of imagined axes: held horizontally, the map is set to a Ptolemaic grid with Europe straddling the Prime Meridian, and yet when held vertically it presents a medieval moral continuum in which the Americas occupy an ascendant position, a verdant new Jerusalem in contrast to the Babylon of the Old World. Europe is both drawn to the centre of a new world order, and also pushed to the moral margins in an echo of the medieval mappa mundi still imperfectly resolved
Peculiarities of phases of the WMAP quadrupole
We present the analysis on the quadrupole phases of the Internal Linear
Combination map, ILC(I) and (III) derived by the WMAP team (1 and 3-year data
release). This approach allows us to see the global trend of non-Gaussianity of
the quadrupoles for the ILC(III) map through phase correlations with the
foregrounds. Significant phase correlations is found in between the ILC(III)
quadrupole and the WMAP foregrounds phases for K-W band: the phases of the
ILC(III) quadrupole xi_{2,1}, xi_{2,2} and those of the foregrounds at K-W
bands Phi_{2,1}, Phi_{2,2} display significant symmetry: xi_{2,1}+Phi_{2,1} ~=
xi_{2,2}+Phi_{2,2}, which is a strong indication that the morphology of the
ILC(III) quadrupole is mere reflection of that the foreground quadrupole
through coupling. To clarify this issue we exploit the symmetry of the CMB
power, which is invariant under permutation of the index m=12. By simple
rotation of the ILC(III) phases with the same angle we reach the phases of
foreground quadrupole. We discuss possible sources of phase correlation and
come to the conclusion that the phases of the ILC(III) quadrupole reflect most
likely systematic effects such as changing of the gain factor for the 3-year
data release with respect to the 1-year, rather than manifestation of the
primordial non-Gaussianity.Comment: 8 pages, 15 page
Prospects for Determining the Equation of State of the Dark Energy: What can be Learned from Multiple Observables?
The dark energy that appears to produce the accelerating expansion of the
universe can be characterized by an equation of state p=w\rho with w<-1/3. A
number of observational tests have been proposed to study the value or redshift
dependence of w, including SN Ia distances, the Sunyaev-Zel'dovich effect,
cluster abundances, strong and weak gravitational lensing, galaxy and quasar
clustering, galaxy ages, the \lya forest, and CMB anisotropies. The proposed
observational tests based on these phenomena measure either the
distance-redshift relation d(z), the Hubble parameter H(z), the age of the
universe t(z), the linear growth factor D_1(z), or some combination of these
quantities. We compute the evolution of these four observables, and of the
combination H(z)d(z) that enters the Alcock-Paczyznski anisotropy test, in
models with constant w, in quintessence models with some simple forms of the
potential V(\phi), and in toy models that allow more radical time variations of
w. Measurement of any of these quantities to precision of a few percent is
generally sufficient to discriminate between w=-1 and w=-2/3. However, the
time-dependence predicted in quintessence models is extremely difficult to
discern because the quintessence component is dynamically unimportant at the
redshifts where w departs substantially from its low-z value. Even for the toy
models that allow substantial changes in w at low redshift, there is always a
constant-w model that produces very similar evolution of all of the observables
simultaneously. We conclude that measurement of the effective equation of state
of the dark energy may be achieved by several independent routes in the next
few years, but that detecting time-variation in this equation of state will
prove very difficult except in specialized cases.Comment: 29 pages, 7 figures, many minor corrections, additions, and
clarifications, to appear in Ap
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