arXiv subjects

R. Tavakol

Publications and source records attributed to R. Tavakol.

24 records · Page 2Linked to original sources

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↗

arXiv1998

The influence of geometry and topology on axisymmetric mean-field dynamos

We study the changes in the dynamical behaviour of axisymmetric spherical mean-field dynamo models produced by changes in their geometry and topology, by considering a two parameter family of models, ranging from a full sphere to spherical shell, torus and disc-like configurations, within a unified framework. We find that the two parameter space of the family of models considered here separates into at least three different regions with distinct characteristics for the onset of dynamo action. In two of these regions, the most easily excited fields are oscillatory, in one case with dipolar symmetry, and in the other with quadrupolar, whereas in the third region the most easily excited field is steady and quadrupolar. In the nonlinear regime, we find that topological changes can alter significantly the dynamical behaviour, whilst modest changes in geometry can produce qualitative changes, particularly for thin disc-like configurations. This is of potential importance, since the exact shapes of astrophysical bodies, especially accretion discs and galaxies, are usually not precisely known.

astro-ph↗

arXiv1998

Mean Field Dynamos with Algebraic and Dynamic alpha-Quenchings

Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic $α$--quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic $α$ appears to be complicated and is affected by the region of parameter space examined.

astro-ph↗

arXiv1998

Dynamics of Axisymmetric Truncated Dynamo Models

An important question regarding the study of mean field dynamo models is how to make precise the nature of their underlying dynamics. This is difficult both because relatively little is known about the dynamical behaviour of infinite dimensional systems and also due to the numerical cost of studying the related partial differential equations. As a first step towards their understanding, it is useful to consider the corresponding truncated models. Here we summarise some recent results of the study of a class of truncated axisymmetric mean field dynamo models. We find conclusive evidence in these models for various types of intermittency as well as multiple attractors and final state sensitivity. We also find that the understanding of the underlying dynamics of such dynamo models requires the study of a new class of dynamical systems, referred to as the {\it non-normal} systems. Current work demonstrates that these types of systems are capable of a novel type of intermittency and also of relevance for the understanding of the full axisymmetric PDE dynamo models.

astro-ph↗

arXiv1998

Effects of anisotropy and spatial curvature on the pre-big bang scenario

A class of exact, anisotropic cosmological solutions to the vacuum Brans-Dicke theory of gravity is considered within the context of the pre-big bang scenario. Included in this class are the Bianchi type III, V and VI_h models and the spatially isotropic, negatively curved Friedmann-Robertson-Walker universe. The effects of large anisotropy and spatial curvature are determined. In contrast to negatively curved Friedmann-Robertson-Walker model, there exist regions of the parameter space in which the combined effects of curvature and anisotropy prevent the occurrence of inflation. When inflation is possible, the necessary and sufficient conditions for successful pre-big bang inflation are more stringent than in the isotropic models. The initial state for these models is established and corresponds in general to a gravitational plane wave.

gr-qc↗