Low power in the cosmic microwave background and its implications for the topology of the universe

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Predicting and analyzing topological correlations in the CMB

The Cosmic Microwave Background (CMB) power spectrum derived from the first year WMAP data demonstrates an intriguing lack of power at large scales that cannot be accounted for within the framework of the standard cosmological model. We explore the possibility that this anomaly could be explained by waiving the implicit assumption of a simply connected topology, rather than modifying the physics of the standard model. In particular, we assume that the Universe is slightly closed and its spatial section can be described by one of the simplest spherical multi-connected manifolds (the quaternionic, the octahedral, the truncated cube and the Poincare space). We discuss the implications for the CMB in each case.Comment: 5 pages, 4 figures. To appear in the proceedings of the 7th astronomy conference of the Hellenic Astronomical Society (8-11 September 2005

A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data

It has been suggested by Roukema and coworkers (hereafter R04) that the topology of the Universe as probed by the ``matched circles'' method using the first year release of the WMAP CMB data, might be that of the Poincar\'e dodecahedral space (PDS) model. An excess in the correlation of the ``identified circles'' was reported by R04, for circles of angular radius of ~11 deg for a relative phase twist -36deg, hinting that this could be due to a Clifford translation, if the hypothesized model were true. R04 did not however specify the statistical significance of the correlation signal. We investigate the statistical significance of the signal using Monte Carlo CMB simulations in a simply connected Universe, and present an updated analysis using the three-year WMAP data. We find that our analyses of the first and three year WMAP data provide results that are consistent with the simply connected space at a confidence level as low as 68%.Comment: 8 pages, 6 figures, typo corrected/replaced to match version published in A&

Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates

We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also studied numerically. Both cases of purely one-dimensional and ``cigar-shaped'' condensates are studied by means of different mean-field models, and the oscillation frequencies of the pertinent solitons are found and compared with the results obtained by the linear stability analysis.Numerical results are shown to be in very good agreement with the corresponding analytical predictions

Cognition, psychopathology and the role of genetic variation in Catechol-O-Methyltransferase in children at increased risk of schizophrenia

In this thesis I explored cognition, psychopathology and the role of Catechol-O-Methyltransferase (COMT) in children at increased risk of schizophrenia with the aim of making a contribution to our understanding of the processes that take place early in the development of psychosis. Two samples were studied. The first sample came from the population-based Avon Longitudinal Study of Parents and Children (ALSPAC) where I examined the relationships between a priori selected cognitive domains and psychotic experiences (PEs). The results indicated that impaired processing speed and attention were related to greater risk of PEs in children, with processing speed being a key cognitive feature. Moreover, the relationships between cognition and later occurrence of PEs were similar to those that have previously been reported between cognition and schizophrenia. I also examined whether genetic variation in COMT was associated with PEs indirectly through cognition and anxiety disorders. The findings showed that COMT was indirectly associated with PEs through processing speed, IQ and attention. The second sample comprised children with 22q11.2 Deletion Syndrome (22q11.2DS). I examined the nature and prevalence of psychopathology and cognitive dysfunction in the sample and their siblings and to what extent the children’s intellectual impairment indirectly influences the risk of psychopathology associated with the deletion. There were high rates of psychopathology and cognitive impairments in children with 22q11.2DS. However, I found no evidence for an indirect association between the deletion and the risk of psychopathology through cognition. Finally, there was no evidence that COMT is related to the susceptibility of children with 22q11.2DS to cognitive and psychiatric problems. These findings have potentially important implications for our understanding of the development of psychosis during childhood and they also show that using different research designs to investigate specific aims in samples at increased risk enables the researcher to widen their scope of interpretation

Imprints of spherical non-trivial topologies on the CMB

The apparent low power in the CMB temperature anisotropy power spectrum derived from WMAP motivated us to consider the possibility of a non-trivial topology. We focus on some simple spherical multi-connected manifolds (Quaternionic, Octahedral, Truncated Cube and Poincare spaces) and discuss their implications for the CMB in terms of the power spectrum, maps and the correlation matrix. We also perform Bayesian model comparison against the fiducial best-fit LCDM based both on the power spectrum and the correlation matrix to assess their statistical significance. We find that the first year power spectrum shows a slight preference for the Truncated Cube space, but the 3-year data show no evidence for any of these spaces.Comment: More comments and references added, results and conclusions unchanged. This version to appear in PR

Some spaces are more equal than others

It has generally been thought that in perturbed Friedmann-Lemaitre-Robertson-Walker models of the Universe, global topology should not have any feedback effects on dynamics. However, a weak-field limit heuristical argument, assuming a finite particle horizon for the transmission of gravitational signals, shows that a residual acceleration effect can occur. The nature of this effect differs algebraically between different constant curvature 3-manifolds. This potentially provides a selection mechanism for the 3-manifold of comoving space.Comment: 4 pages, proceedings of the Grassmannian Conference in Fundamental Cosmology, Szczecin, 14-19 Sep 2009, to be refereed by Annalen der Physi

The power of Bayesian evidence in astronomy

We discuss the use of the Bayesian evidence ratio, or Bayes factor, for model selection in astronomy. We treat the evidence ratio as a statistic and investigate its distribution over an ensemble of experiments, considering both simple analytical examples and some more realistic cases, which require numerical simulation. We find that the evidence ratio is a noisy statistic, and thus it may not be sensible to decide to accept or reject a model based solely on whether the evidence ratio reaches some threshold value. The odds suggested by the evidence ratio bear no obvious relationship to the power or Type I error rate of a test based on the evidence ratio. The general performance of such tests is strongly affected by the signal to noise ratio in the data, the assumed priors, and the threshold in the evidence ratio that is taken as `decisive'. The comprehensiveness of the model suite under consideration is also very important. The usefulness of the evidence ratio approach in a given problem can be assessed in advance of the experiment, using simple models and numerical approximations. In many cases, this approach can be as informative as a much more costly full-scale Bayesian analysis of a complex problem.Comment: 11 pages; MNRAS in pres