Detectability of Cosmic Topology in Flat Universes

Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We first give a complete description of the diffeomorphic classification of compact flat 3-manifolds, and derive the expressions for the injectivity radii, and for the volume of each class of Euclidean 3-manifolds. There emerges from our calculations the undetectability conditions for each (topological) class of flat universes. To illustrate the detectability of flat topologies we construct toy models by using an assumption by Bernshtein and Shvartsman which permits to establish a relation between topological typical lengths to the dynamics of flat models.Comment: 17 pages, 1 figure, latex2e. New references added. Inserted clarifying points. To appear in Phys. Lett. A (2003) in the present for

A method to search for topological signatures in the angular distribution of cosmic objects

We present a method to search for large angular-scale correlations, termed topological signatures, in the angular distribution of cosmic objects, which does not depend on cosmological models or parameters and is based only on the angular coordinates of the objects. In order to explore Cosmic Microwave Background temperature fluctuations data, we applied this method to simulated distributions of objects in thin spherical shells located in three different multiply-connected Euclidean 3-spaces ($T^3$, $T_{\pi}$, and $G_6$), and found that the topological signatures due to these topologies can be revealed even if their intensities are small. We show how to detect such signatures for the cases of full-sky and partial-sky distributions of objects. This method can also be applied to other ensembles of cosmic objects, like galaxies or quasars, in order to reveal possible angular-scale correlations in their distributions.Comment: 11 pages, 18 figures. To appear in A&

Topological signatures in CMB temperature anisotropy maps

We propose an alternative formalism to simulate CMB temperature maps in $\Lambda$CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial sections. Instead, the covariance matrix of the coefficients of the spherical harmonic decomposition of the temperature anisotropies is expressed in terms of the elements of the covering group of the space. We obtain a decomposition of the correlation matrix that isolates the topological contribution to the CMB temperature anisotropies out of the simply connected contribution. A further decomposition of the topological signature of the correlation matrix for an arbitrary topology allows us to compute it in terms of correlation matrices corresponding to simpler topologies, for which closed quadrature formulae might be derived. We also use this decomposition to show that CMB temperature maps of (not too large) multiply connected universes must show ``patterns of alignment'', and propose a method to look for these patterns, thus opening the door to the development of new methods for detecting the topology of our Universe even when the injectivity radius of space is slightly larger than the radius of the last scattering surface. We illustrate all these features with the simplest examples, those of flat homogeneous manifolds, i.e., tori, with special attention given to the cylinder, i.e., $T^1$ topology.Comment: 25 pages, 7 eps figures, revtex4, submitted to PR

Can We See the Shape of the Universe?

This is a written version of a talk given at the Fifth Friedmann Seminar on recent work in Observational Cosmic Topology done in partial collaboration with Armando Bernui. We address three relevant questions related to the search for the size and shape of our Universe: (i) How do the actual observation of multiple images of certain cosmic objects, e.g. galaxy clusters, constrain the possible models for the shape of our Universe?, (ii) What kind of predictions can be done once a pair of cosmic objects have been identified to be topological images related by a translation?, and (iii) Is it possible to determine if two regions of space are topologically identified, even when distortions on the distributions of cosmic sources due to observational limitations are not negligible? We give examples answering the first two questions using the suggestion of Roukema and Edge that the clusters RXJ 1347.5-1145 and CL 09104+4109 might be topological images of the Coma cluster. For the third question, we suggest a method based on the analysis of PSH's noise correlations which seems to give a positive answer.Comment: 6 pages, latex2e, contribution to the 5th Alexander Friedmann Seminar on Gravitation and Cosmology, to appear in Int. J. Mod. Phys. A (2002). Macros: ws-ijmpa.cl

Spikes in Cosmic Crystallography

If the universe is multiply connected and small the sky shows multiple images of cosmic objects, correlated by the covering group of the 3-manifold used to model it. These correlations were originally thought to manifest as spikes in pair separation histograms (PSH) built from suitable catalogues. Using probability theory we derive an expression for the expected pair separation histogram (EPSH) in a rather general topological-geometrical-observational setting. As a major consequence we show that the spikes of topological origin in PSH's are due to translations, whereas other isometries manifest as tiny deformations of the PSH corresponding to the simply connected case. This result holds for all Robertson-Walker spacetimes and gives rise to two basic corollaries: (i) that PSH's of Euclidean manifolds that have the same translations in their covering groups exhibit identical spike spectra of topological origin, making clear that even if the universe is flat the topological spikes alone are not sufficient for determining its topology; and (ii) that PSH's of hyperbolic 3-manifolds exhibit no spikes of topological origin. These corollaries ensure that cosmic crystallography, as originally formulated, is not a conclusive method for unveiling the shape of the universe. We also present a method that reduces the statistical fluctuations in PSH's built from simulated catalogues.Comment: 25 pages, LaTeX2e. References updated. To appear in Int. J. Mod. Phys. D (2002) in the present for

Latin Hypercube Sampling and Partial Rank Correlation Coefficient Analysis Applied to an Optimal Control Problem

Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis is an efficient tool often employed in uncertainty analysis to explore the entire parameter space of a model. Despite the usefulness of LHS/PRCC sensitivity analysis in studying the sensitivity of a model to the parameter values used in the model, no study has been done that fully integrates Latin Hypercube sampling with optimal control analysis. In this thesis, we couple the optimal control numerical procedure to the LHS/PRCC procedure and perform a simultaneous examination of the effects of all the LHS parameter on the objective functional value. To test the effectiveness of our procedure, we examine the sensitive parameters in a deterministic ordinary differential equations cholera model having seven human compartments and two bacterial compartments. Our procedure cuts down on simulation time and helps us perform a more comprehensive analysis of the influential parameters in the cholera model, than would be possible otherwise

Evaluación de la actividad antielastasa, antihialuronidasa y antioxidante del fruto de tres variedades de uva (Vitis vinifera)

Publicación a texto completo no autorizada por el autorDetermina la capacidad de inhibición de las enzimas elastasa, hialuronidasa y la capacidad antioxidante por parte del fruto de tres variedades de uva (Vitis vinífera), negra (borgoña), roja (red globe) y verde (Italia). Se procesó seis tipos de muestra, dos de cada variedad, una con semillas (CS) y otra sin semillas (SS) licuando por un minuto 100 g. de cada uno de ellos agregando 100 mL de agua destilada y filtrando luego hasta obtener los primeros 100 mL de filtrado de cada muestra para finalmente centrifugar a 15 000 G por 15 minutos. Cada uno de los extractos obtenidos se utilizó para la determinación de polifenoles totales, determinación de la capacidad de inhibción de la enzima elastasa y de la enzima hialuronidasa y determinación de la capacidad antioxidante. Se pudo determinar que en cada uno de los 100 mL de extracto acuoso, en la uva negra con semillas existe mayor cantidad de compuestos polifenólicos, 55 mg equivalentes de ácido gálico (AGE), seguido de la uva roja con 35 mg AGE y luego la uva verde con 21 mg AGE; mientras que en la determinación de la capacidad de inhibición de la enzima elastasa, es la uva roja quien destaca con un porcentaje de inhibición de 57,52 %, seguida de la uva negra con 50,53 % y después la uva verde con 30,59 %; en la determinación de la capacidad de inhibición de la enzima hialuronidasa a los 30 minutos, es la uva negra quien logra un mayor porcentaje de inhibición, 32,46 %, seguida de la uva roja con 18,22 % y al final la uva verde con 9,32 %; de forma similar resulta la determinación de la capacidad antioxidante donde también es la uva negra la que presenta mayor efecto alcanzando un valor de 0,2298 mg Fe2+ , luego la uva roja con 0,1417 mg Fe2+, y por último la uva verde con 0,0689 mg Fe2+ , (Tabla 15). Es preciso señalar que para cada una de las determinaciones con respecto a una misma variedad de uva siempre se encuentra mayor actividad en las muestras procesadas con semilla.Tesi