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M. J. Reboucas

Publications and source records attributed to M. J. Reboucas.

At least 73 records · Page 4Linked to original sources
arXiv2004

Consequences of Observational Uncertainties on the Detection of Cosmic Topology

The observed values of density parameters inevitably involve uncertainties. We study the conditions for detectability and undetectability of cosmic topology in presence of such uncertainties. We present closed analytical forms of (un)detectability conditions for infinite redshift, which are important because: (i) they allow the examine of the detectability of cosmic topology not only for individual manifolds (topologies), but also in whole classes of manifolds; (ii) they are, to a very good approximation, (un)detectibility conditions for z=1100.

astro-ph↗
arXiv2004

Cosmic Topology: a Brief Overview

Questions such as whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental open problems that high precision modern cosmology needs to resolve. These questions go beyond the scope of general relativity (GR), since as a (local) metrical theory GR leaves the global topology of the universe undetermined. Despite our present-day inability to predict the topology of the universe, given the wealth of increasingly accurate astro-cosmological observations it is expected that we should be able to detect it. An overview of basic features of cosmic topology, the main methods for its detection, and observational constraints on detectability are briefly presented. Recent theoretical and observational results related to cosmic topology are also discussed.

astro-ph↗
arXiv2003

Classification of Energy Momentum Tensors in $n \geq 5$ Dimensional Space-times: a Review

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of a great number of brane cosmological models is that in which the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we review the main results on the algebraic classification of second order symmetric tensors in 5-dimensional space-times. All possible Segre types for a symmetric two-tensor are found, and a set of canonical forms for each Segre type is obtained. A limiting diagram for the Segre types of these symmetric tensors in 5-D is built. Two theorems which collect together some basic results on the algebraic structure of second order symmetric tensors in 5-D are presented. We also show how one can obtain, by induction, the classification and the canonical forms of a symmetric two-tensor on n-dimensional (n > 5) spaces from its classification in 5-D spaces, present the Segre types in n-D and the corresponding canonical forms. This classification of symmetric two-tensors in any n-D spaces and their canonical forms are important in the context of n-dimensional brane-worlds context and also in the framework of 11-D supergravity and 10-D superstrings.

gr-qc↗
arXiv2003

A Note on Segre Types of Second Order Symmetric Tensors in 5-D Brane-world Cosmology

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of most brane cosmological models is that in which the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we reexamine the classification of the second order symmetric tensors in 5--D, and prove two theorems which collect together some basic results on the algebraic structure of these tensors in 5-dimensional space-times. We also briefly indicate how one can obtain, by induction, the classification of symmetric two-tensors (and the corresponding canonical forms) on n-dimensional spaces from the classification on 4-dimensional spaces. This is important in the context of 11--D supergravity and 10--D superstrings.

gr-qc↗
arXiv2003

Constraints on the Detectability of Cosmic Topology from Observational Uncertainties

Recent observational results suggest that our universe is nearly flat and well modelled within a $Λ$CDM framework. The observed values of $Ω_{m}$ and $Ω_Λ$ inevitably involve uncertainties. Motivated by this, we make a systematic study of the necessary and sufficient conditions for undetectability as well as detectability (in principle) of cosmic topology (using pattern repetition) in presence of such uncertainties. We do this by developing two complementary methods to determine detectability for nearly flat universes. Using the first method we derive analytical conditions for undetectability for infinite redshift, the accuracy of which is then confirmed by the second method. Estimates based on WMAP data together with other measurements of the density parameters are used to illustrate both methods, which are shown to provide very similar results for high redshifts.

gr-qc↗
arXiv2003

What do very nearly flat detectable cosmic topologies look like?

Recent studies of the detectability of cosmic topology of nearly flat universes have often concentrated on the range of values of $Ω_{0}$ given by current observations. Here we study the consequences of taking the bounds on $Ω_{0}$ given by inflationary models, i.e. $|Ω_0 - 1| \ll 1$. We show that in this limit, a generic detectable non-flat manifold is locally indistinguishable from either a cylindrical ($R^2 \times S^1$) or toroidal ($R \times T^2$) manifold, irrespective of its global shape, with the former being more likely. Importantly this is compatible with some recent indications based on the analysis of high resolution CMB data. It also implies that in this limit an observer would not be able to distinguish topologically whether the universe is spherical, hyperbolic or flat. By severely restricting the expected topological signatures of detectable isometries, our results provide an effective theoretical framework for interpreting cosmological observations, and can be used to confine any parameter space which realistic search strategies, such as the `circles in the sky' method, need to concentrate on. This is particularly important in the inflationary limit, where the precise nature of cosmic topology becomes undecidable.

astro-ph↗
arXiv2003

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.

gr-qc↗
arXiv2002

Limits on the Detectability of Cosmic Topology in Hyperbolic Universes

We reexamine the possibility of the detection of the cosmic topology in nearly flat hyperbolic Friedmann-Lemaitre-Robertson-Walker (FLRW) universes by using patterns repetition. We update and extend our recent results in two important ways: by employing recent observational constraints on the cosmological density parameters as well as the recent mathematical results concerning small hyperbolic 3-manifolds. This produces new bounds with consequences for the detectability of the cosmic topology. In addition to obtaining new bounds, we also give a concrete example of the sensitive dependence of detectability of cosmic topology on the uncertainties in the observational values of the density parameters.

gr-qc↗
arXiv2002

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.

gr-qc↗
arXiv2001

Are Small Hyperbolic Universes Observationally Detectable?

Using recent observational constraints on cosmological density parameters, together with recent mathematical results concerning small volume hyperbolic manifolds, we argue that, by employing pattern repetitions, the topology of nearly flat small hyperbolic universes can be observationally undetectable. This is important in view of the facts that quantum cosmology may favour hyperbolic universes with small volumes, and from the expectation coming from inflationary scenarios, that $Ω_0$ is likely to be very close to one.

gr-qc↗
arXiv2001

Detectability of Cosmic Topology in Almost Flat Universes

Recent observations suggest that the ratio of the total density to the critical density of the universe, $Ω_0$, is likely to be very close to one, with a significant proportion of this energy being in the form of a dark component with negative pressure. Motivated by this result, we study the question of observational detection of possible non-trivial topologies in universes with $Ω_0 \sim 1$, which include a cosmological constant. Using a number of indicators we find that as $Ω_0 \to 1$, increasing families of possible manifolds (topologies) become either undetectable or can be excluded observationally. Furthermore, given a non-zero lower bound on $|Ω_0 - 1|$, we can rule out families of topologies (manifolds) as possible candidates for the shape of our universe. We demonstrate these findings concretely by considering families of topologies and employing bounds on cosmological parameters from recent observations. We find that given the present bounds on cosmological parameters, there are families of both hyperbolic and spherical manifolds that remain undetectable and families that can be excluded as the shape of our universe. These results are of importance in future search strategies for the detection of the shape of our universe, given that there are an infinite number of theoretically possible topologies and that the future observations are expected to put a non-zero lower bound on $|Ω_0 - 1|$ which is more accurate and closer to zero.

gr-qc↗
arXiv2001

Signature for the Shape of the Universe

If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to reveal the topological signature of any Robertson-Walker (RW) spacetime with nontrivial topology. We also show through computer-aided simulations how one can extract the topological signatures of flat, elliptic, and hyperbolic RW universes with nontrivial topology.

gr-qc↗
arXiv2001

A Topological Signature in Cosmic Topology

Two procedures for obtaining (extracting and constructing) the topological signature of any multiply connected Robertson-Walker (RW) universe are presented. It is shown through computer-aided simulations that both approaches give rise to the same topological signature for a multiply connected flat RW universe. The strength of these approaches is illustrated by extracting the topological signatures of a flat ($k=0$), an elliptic ($k=1$), and a hyperbolic ($k=-1$) multiply connected RW universes. We also show how separated contributions of the covering isometries add up to form the topological signature of a RW flat universe. There emerges from our theoretical results and simulations that the topological signature arises (in the mean) even when there are just a few images for each object. It is also shown that the mean pair separation histogram technique works, and that it is a suitable approach for studying the topological signatures of RW universes as well as the role of non-translational isometries.

gr-qc↗
arXiv2000

Topological Reverberations in Flat Space-times

We study the role played by multiply-connectedness in the time evolution of the energy E(t) of a radiating system that lies in static flat space-time manifolds M_4 whose t=const spacelike sections M_3 are compact in at least one spatial direction. The radiation reaction equation of the radiating source is derived for the case where M_3 has any non-trivial flat topology, and an exact solution is obtained. We also show that when the spacelike sections are multiply-connected flat 3-manifolds the energy E(t) exhibits a reverberation pattern with discontinuities in the derivative of E(t) and a set of relative minima and maxima, followed by a growth of E(t). It emerges from this result that the compactness in at least one spatial direction of Minkowski space-time is sufficient to induce this type of topological reverberation, making clear that our radiating system is topologically fragile. An explicit solution of the radiation reaction equation for the case where M_3 = R^2 x S^1 is discussed, and graphs which reveal how the energy varies with the time are presented and analyzed.

gr-qc↗
arXiv2000

Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes

We study the topological signature of euclidean isometries in pair separations histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing the noise of individual PSH's using mean pair separations histograms we show how to distinguish between topological and statistical spikes. We report results of simulations that evince that topological spikes are not enough to distinguish between manifolds with the same set of Clifford translations in their covering groups, and that they are not the only signature of topology in PSH's corresponding to euclidean small universes. We also show how to evince the topological signature due to non-translational isometries.

gr-qc↗
arXiv2000

Distinguishing Marks of Simply-connected Universes

A statistical quantity suitable for distinguishing simply-connected Robertson-Walker (RW) universes is introduced, and its explicit expressions for the three possible classes of simply-connected RW universes with an uniform distribution of matter are determined. Graphs of the distinguishing mark for each class of RW universes are presented and analyzed.There sprout from our results an improvement on the procedure to extract the topological signature of multiply-connected RW universes, and a refined understanding of that topological signature of these universes studied in previous works.

gr-qc↗
arXiv1999

Gödel-type Spacetimes in Induced Matter Gravity Theory

A five-dimensional (5D) generalized Gödel-type manifolds are examined in the light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by three essential parameters $k$, $m^2$ and $ω$: identical triads $(k, m^2, ω)$ correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian generalized Gödel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that the generalized Gödel-type 5D manifolds admit maximal group of isometry $G_r$ with $r=7$, $r=9$ or $r=15$ depending on the essential parameters $k$, $m^2$ and $ω$. The breakdown of causality in all these classes of homogeneous Gödel-type manifolds are also examined. It is found that in three out of the six irreducible classes the causality can be violated. The unique generalized Gödel-type solution of the induced matter (IM) field equations is found. The question as to whether the induced matter version of general relativity is an effective therapy for these type of causal anomalies of general relativity is also discussed in connection with a recent article by Romero, Tavakol and Zalaletdinov.

gr-qc↗