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

On the Green and Wald formalism

Backreaction in the cosmological context is a longstanding problem that is especially important in the present era of precise cosmology. The standard model of a homogeneous background plus density perturbations is most probably oversimplified and is expected to fail to fully account for the near-future observations of sub-percent precision. From a theoretical point of view, the problem of backreaction is very complicated and deserves careful examination. Recently, Green and Wald claimed in a series of papers to have developed a formalism to properly describe the influence of density inhomogeneities on average properties of the Universe, i.e., the backreaction effect. A brief discussion of this framework is presented, focussing on its drawbacks and on misconceptions that have arisen during the "backreaction debate".Comment: Contribution to the proceedings of MG1

Does gravity prefer the Poincare dodecahedral space?

The missing fluctuations problem in cosmic microwave background observations is naturally explained by well-proportioned small universe models. Among the well-proportioned models, the Poincare dodecahedral space is empirically favoured. Does gravity favour this space? The residual gravity effect is the residual acceleration induced by weak limit gravity from multiple topological images of a massive object on a nearby negligible mass test object. At the present epoch, the residual gravity effect is about a million times weaker in three of the well-proportioned spaces than in ill-proportioned spaces. However, in the Poincare space, the effect is 10,000 times weaker still, i.e. the Poincare space is about 10^{10} times "better balanced" than ill-proportioned spaces. Both observations and weak limit dynamics select the Poincare space to be special.Comment: 6 pages, Honorable Mention in 2009 Gravity Research Foundation essay competitio

On the relativistic mass function and averaging in cosmology

The general relativistic description of cosmological structure formation is an important challenge from both the theoretical and the numerical point of views. In this paper we present a brief prescription for a general relativistic treatment of structure formation and a resulting mass function on galaxy cluster scales in a highly generic scenario. To obtain this we use an exact scalar averaging scheme together with the relativistic generalization of Zel'dovich's approximation (RZA) that serves as a closure condition for the averaged equations.Comment: Contribution to the proceedings of MG1

Correspondences - Online Journal For The Academic Study of Western Esotericism, Volume 2.2

Welcome to Correspondences, an international, peer-reviewed online journal devoted to the academic study of Western esotericism. By providing a wider forum of debate regarding issues and currents in Western esotericism than has previously been possible, Correspondences is committed to publishing work of a high academic standard as determined by a peer-review process, but does not require academic credentials as prerequisite for publication. Students and non-affiliated academics are encouraged to join established scholars in submitting insightful, well-researched articles that offer new ideas, positions, or information to the field

Deep redshift topological lensing: strategies for the T^3 candidate

The 3-torus (T^3) FLRW model better fits the nearly zero large-scale auto-correlation of the WMAP CMB sky maps than the infinite flat model. The T^3 model's WMAP parameters imply approximately equal-redshift topological lensing at z \sim 6. We investigate observational strategies for rejecting the T^3 solution or providing candidate topologically lensed galaxy pairs. T^3 holonomies are applied to (i) existing z \sim 6 observations and (ii) simulated observations, creating multiply connected catalogues. Corresponding simply connected catalogues are generated. Each catalogue is analysed using a successive filter method and collecting matched quadruples. Quadruple statistics between the multiply and simply connected catalogues are compared. The expected rejection of the hypothesis, or detection of candidate topologically lensed galaxies, is possible at a significance of 5% for a pair of T^3 axis-centred northern and southern surveys if photometric redshift accuracy is \sigma(\zphot) < 0.01 for a pair of nearly complete 100 deg^2 surveys with a total of > 500 galaxies over 4.3 < z < 6.6, or for a pair of 196 deg^2 surveys with > 400 galaxies and \sigma(\zphot) < 0.02 over 4<z<7. Dropping the maximum time interval in a pair from \Delta t =1 Gyr/h to \Delta t =0.1 Gyr/h yields a requirement of \sigma(\zphot) < 0.005 or \sigma(\zphot) < 0.01, respectively. Millions of z \sim 6 galaxies will be observed over fields of these sizes during the coming decades, implying much stronger constraints. The question is not if the hypothesis will be rejected or confirmed, it is when.Comment: 13 pages, 9 figures, 5 tables, MNRAS, accepte

Effect of Surgery on Quality of Life with Operable Breast Cancer in Limited Resource Environments: Reply

Ó The Author(s) 2010. This article is published with open access at Springerlink.com We thank Purvi Thakkar et al. for their comments on our article [1]. It is good to see that our results are reproducible. The reported decrease in quality of life may be explained by the fact that a different questionnaire was used. The FACT-B is a disease-specific questionnaire that inquires more into functioning than into satisfaction with functioning. The primary goal of our study was to present surgeons with other factors than only the clinical parameters, such as tumor size, that can help in the decisional process. We hope that more surgeons will assess the personality of a woman with early-stage breast cancer and use this as additional information when counseling her about possible breast cancer treatment modalities. Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited