Talking About Singularities (2007)
We discuss some aspects of recent research as well as more general issues about motivation, useful methods and open problems in the field of cosmological singularities. In particular, we review some...
Asymptotics of flat, radiation universes in quadratic gravity (2007)
Cotsakis, Spiros, Tsokaros, Antonios
We consider the asymptotics of flat, radiation-dominated isotropic universes in four-dimensional theories with quadratic curvature corrections which may arise when contributions related to the string...
Braneworld cosmological singularities (2007)
Antoniadis, Ignatios, Cotsakis, Spiros, Klaoudatou, Ifigeneia
The purpose of this brief report is to present some results of our on-going project on the asymptotic behaviour of braneworld-type solutions on approach to their possible finite `time' singularities.
Flat, radiation universes with quadratic corrections and asymptotic analysis (2006)
Cotsakis, Spiros, Tsokaros, Antonios
It was shown long ago by T. V. Ruzmaikina and A. A. Ruzmaikin that within the framework of a homogeneous and isotropic cosmological model quadratic corrections of the gravitational field cannot...
Singularities of varying light speed cosmologies (2006)
Miritzis, John, Cotsakis, Spiros
We study the possible singularities of isotropic cosmological models that have a varying speed of light as well as a varying gravitational constant. The field equations typically reduce to two...
Bel-Robinson energy and the nature of singularities in isotropic cosmologies (2006)
Klaoudatou, Ifigeneia, Cotsakis, Spiros
We review our recent work on the classification of finite time singularities that arise in isotropic universes. This scheme is based on the exploitation of the Bel Robinson energy in a cosmological...
The Dominant Balance at Cosmological Singularities (2006)
Cotsakis, Spiros, Barrow, John D.
We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of...
Future Singularities and Completeness in Cosmology (2006)
We review recent work on the existence and nature of cosmological singularities that can be formed during the evolution of generic as well as specific cosmological spacetimes in general relativity....
Cosmological Singularities and Bel-Robinson Energy (2006)
Cotsakis, Spiros, Klaoudatou, Ifigeneia
We consider the problem of describing the asymptotic behaviour of \textsc{FRW} universes near their spacetime singularities in general relativity. We find that the Bel-Robinson energy of these...
Singular Isotropic Cosmologies and Bel-Robinson Energy (2006)
Cotsakis, Spiros, Klaoudatou, Ifigeneia
We consider the problem of the nature and possible types of spacetime singularities that can form during the evolution of \emph{FRW} universes in general relativity. We show that by using, in...
Slice Energy and Theories of Gravitation (2005)
We review recent work on the use of the slice energy concept in generalized theories of gravitation. We focus on two special features in these theories, namely, the energy exchange between the matter...
Modern Approaches to Cosmological Singularities (2005)
Cotsakis, Spiros, Klaoudatou, Ifigeneia
We review recent work and present new examples about the character of singularities in globally and regularly hyperbolic, isotropic universes. These include recent singular relativistic models,...
Slice Energy and Conformal Frames in Theories of Gravitation (2004)
We examine and compare the behaviour of the scalar field slice energy in different classes of theories of gravity, in particular higher-order and scalar-tensor theories. We find a universal formula...
Future Singularities of Isotropic Cosmologies (2004)
Cotsakis, Spiros, Klaoudatou, Ifigeneia
We show that globally and regularly hyperbolic future geodesically incomplete isotropic universes, except for the standard all-encompassing `big crunch', can accommodate singularities of only one...
Slice Energy in Higher Order Gravity Theories and Conformal Transformations (2004)
We study the generic transport of slice energy between the scalar field generated by the conformal transformation of higher-order gravity theories and the matter component. We give precise relations...
Symmetries of homogeneous cosmologies (2004)
Cotsakis, Spiros, Leach, P. G. L., Pantazi, Chara
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self- interaction potential in the language of jet bundles and extensions of vector fields....
Symmetries of homogeneous cosmologies (2004)
Cotsakis, Spiros, Leach, P. G. L., Pantazi, Chara
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-interaction potential in the language of jet bundles and extensions of vector fields....
Symmetries of homogeneous cosmologies (2004)
Cotsakis, Spiros, Leach, P. G. L., Pantazi, Chara
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self- interaction potential in the language of jet bundles and extensions of vector fields....
Global Hyperbolicity of Sliced Spaces (2003)
We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us...
Cosmological Singularities (2002)
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand...
Global Hyperbolicity and Completeness (2002)
Choquet-Bruhat, Yvonne, Cotsakis, Spiros
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the...
A note on wavemap-tensor cosmologies (2001)
Cotsakis, Spiros, Miritzis, John
We examine theories of gravity which include finitely many coupled scalar fields with arbitrary couplings to the curvature (wavemaps). We show that the most general scalar-tensor $\sigma$-model...
Current Trends in Mathematical Cosmology (2001)
We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of...
Leach, Peter, Cotsakis, Spiros, Miritzis, John
This paper considers some physically interesting cosmological dynamical systems in the FRW-scalarfield category which are examined for integrability according to the criterion of Painlev\'e. In the...
Cotsakis, Spiros, Leach, Peter
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the...
Algebraic integrability of FRW-scalar cosmologies (2000)
Cotsakis, Spiros, Miritzis, John
For dynamical systems of dimension three or more the question of integrability or nonintegrability is extended by the possibility of chaotic behaviour in the general solution. We determine the...
Scalar-tensor $\sigma$-cosmologies (2000)
Cotsakis, Spiros, Miritzis, John
We show that the scalar-tensor $\sigma$-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold...
Symmetries of homogeneous cosmologies (2000)
Cotsakis, Spiros, Leach, Peter, Pantazi, Hara
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-interaction potential in the language of jet bundles and extensions of vector fields....
Ever-expanding, Isotropizing, Quadratic Cosmologies (2000)
Cotsakis, Spiros, Flessas, George, Leach, Peter, Querella, Laurent
We consider some aspects of the global evolution problem of Hamiltonian homogeneous, anisotropic cosmologies derived from a purely quadratic action functional of the scalar curvature. We show that...
Miritzis, John, Leach, Peter, Cotsakis, Spiros
We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory with a variety of matter terms. For some of these models the standard...
Leach, Peter, Cotsakis, Spiros, Flessas, George
The explicit integrability of second order ordinary differential equations invariant under time-translation and rescaling is investigated. Quadratic systems generated from the linearisable version of...
Leach, Peter, Moyo, Sibusio, Cotsakis, Spiros, Lemmer, R. L.
The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether...
Symmetry, singularities and integrability in complex dynamics I: the reduction problem (2000)
Leach, Peter, Cotsakis, Spiros, Flessas, George P.
Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlev\'e property as the number of equations in each...
Cosmological models in higher-order gravity. (1990)
Thesis (Ph. D.)--University of Sussex, 1990.