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 $\phi$, found by maximising \ximc relative to \xisc in the WMAP maps, should yield $\phi \in \{\pm 36\deg\}$. 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 $\phi$. 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 $(l,b)_{i=1,6}\approx (184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d, -4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution has twist \phi= (+39 \pm 2.5)d, in agreement with the PDS model. The chance of this occurring in the simply connected model, assuming a uniform distribution$\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 $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ 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 $\alpha$ than using the twist angle $\phi$. The best estimate of $\alpha$ 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 $\phi$ from the GRF simulations is approximately Gaussian around zero, it is not uniform on $[-\pi,\pi]$. 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