arXiv subjects

Spiros Cotsakis

Publications and source records attributed to Spiros Cotsakis.

At least 55 records · Page 3Linked to original sources

arXiv2014

Enveloping branes and braneworld singularities

The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows to determine the singularity structure of the solutions. The result is applied to braneworlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parametrizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite distance singularity contrary to previous claims. We then study the possibility of avoiding finite distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes however this possibility, as well.

hep-th↗

arXiv2013

Flat limits of curved interacting cosmic fluids

We study curved isotropic cosmologies filled with two interacting fluids near their time singularities. We find that a number of these universes asymptote to flat limits in the sense that their asymptotic properties become indistinguishable from those of flat Friedmann-Robertson-Walker models on approach to the singularity along any asymptotic direction. In particular, there are no essential singularities in these models. We discuss connections of this result with possible extensions of the cosmic no hair theorem to the case of two interacting fluids, and also provide links to a quantum cosmological treatment of real and complex Euclidean such solutions.

gr-qc↗

arXiv2013

Asymptotic Poincaré compactification and finite-time singularities

We provide an extension of the method of asymptotic decompositions of vector fields with finite-time singularities by applying the central extension technique of Poincaré to the dominant part of the vector field on approach to the singularity. This leads to a bundle of fan-out asymptotic systems whose equilibria at infinity govern the dynamics of the asymptotic solutions of the original system. We show how this method can be useful to describe a single-fluid isotropic universe at the time of maximum expansion, and discuss possible relations of our results to structural stability and non-compact phase spaces.

gr-qc↗

arXiv2013

The initial state of generalized radiation universes

We use asymptotic methods to study the early time stability of isotropic and homogeneous solutions filled with radiation which are close initially to the exact, flat, radiation solution in quadratic lagrangian theories of gravity. For such models, we analyze all possible modes of approach to the initial singularity and prove the essential uniqueness and stability of the resulting asymptotic scheme in all cases except perhaps that of the conformally invariant Bach-Weyl gravity. We also provide a formal series representation valid near the initial singularity of the general solution of these models and show that this is dominated at early times by a form in which both curvature and radiation play a subdominant role. We also discuss the implications of these results for the generic initial state of the theory.

gr-qc↗

arXiv2013

Generic regular universes in higher order gravity theories

We review recent results on the Cauchy-Kowalevsky structure of theories with higher derivatives in vacuum. We prove genericity of regularity of solutions under the assumption of analyticity. Our approach is framed in the general context of formal series expansions of the metric around a regular point.

gr-qc↗

arXiv2013

Asymptotic states of generalized universes with higher derivatives

We review ongoing research related to the asymptotic dynamics of isotropic universes in theories with higher derivatives, especially near the initial singularity. We treat two major cases, that is universes in vacuum, and also those filled with radiation using the method of asymptotic splittings of vector fields. Our solutions have the form of formal Fuchsian-type series for the basic unknowns and are valid near collapse or big rip regimes asymptotically.

gr-qc↗

arXiv2013

Limits of isotropic universes with interacting fluids

We find various asymptotic limits of universes containing two interacting fluids which interact and exchange energy. We study the finite-time singularities that may develop in these cosmologies and obtain the asymptotic behaviours of the solutions near such blow up regimes.

gr-qc↗

arXiv2013

Structure of infinity in cosmology

We discuss recent developments related to certain blow up methods suitable for the analysis of cosmological singularities and asymptotics. We review results obtained in a variety of currently popular themes and describe ongoing research about universes with various kinds of extreme states, higher order gravity, and certain models of braneworlds.

gr-qc↗

arXiv2012

Brane singularities with mixtures in the bulk

By extending previous analysis of the authors, a systematic study of the singularity structure and possible asymptotic behaviors of five-dimensional braneworld solutions is performed in the case where the bulk is a mixture of an analog of perfect fluid (with a density and pressure depending on the extra coordinate) and a massless scalar field. The two bulk components interact by exchanging energy so that the total energy is conserved. In a particular range of the interaction parameters, we find flat brane general solutions avoiding the singularity at finite distance from the brane, in the same region of the equation of state constant parameter $γ=P/ρ$ that we found previously in the absence of the bulk scalar field $(-1<γ<-1/2)$.

hep-th↗

arXiv2012

Singularities in cosmologies with interacting fluids

We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally around the spacetime singularity. We find the attractor of all solutions with standard decay, and for `phantom' matter asymptotically at early times. We give a number of special asymptotic solutions describing universes collapsing to zero size and others ending at a big rip singularity. We also find a very complicated singularity corresponding with a logarithmic branch point that resembles of cyclic universe, and give an asymptotic local series representation of the general solution in the neighborhood of infinity.

gr-qc↗

arXiv2010

Brane singularities and their avoidance in a fluid bulk

Using the method of asymptotic splittings, the possible singularity structures and the corresponding asymptotic behavior of a 3-brane in a five-dimensional bulk are classified, in the case where the bulk field content is parametrized by an analog of perfect fluid with an arbitrary equation of state $P=γρ$ between the `pressure' $P$ and the `density' $ρ$. In this analogy with homogeneous cosmologies, the time is replaced by the extra coordinate transverse to the 3-brane, whose world-volume can have an arbitrary constant curvature. The results depend crucially on the constant parameter $γ$: (i) For $γ>-1/2$, the flat brane solution suffers from a collapse singularity at finite distance, that disappears in the curved case. (ii) For $γ<-1$, the singularity cannot be avoided and it becomes of the type big rip for a flat brane. (iii) For $-1<γ\le -1/2$, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility for a revival of the self-tuning proposal.

hep-th↗

arXiv2010

Brane singularities with a scalar field bulk

The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field in a five dimensional bulk is analyzed in full generality, using the method of asymptotic splittings. It is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved.

gr-qc↗

arXiv2008

Slice Energy in Higher Order Gravity Theories and Conformal Transformations

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 for this exchange in the cases of dust and perfect fluids. We show that, unless we are in a stationary spacetime where slice energy is always conserved, in non-stationary situations contributions to the total slice energy depend on whether or not test matter follows geodesics in both frame representations of the dynamics, that is on whether or not the two conformally related frames are physically indistinguishable.

gr-qc↗

arXiv2007

Asymptotics of flat, radiation universes in quadratic gravity

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 parameter $α'$ are switched on. We show that all such universes are singular initially, and calculate all early time asymptotics using the method of asymptotic splittings. We also examine the late time asymptotic behaviour of these models and show that there are no solutions which diverge as $e^{t^2}$, the known radiation solution of general relativity is essentially the only late time asymptotic possibility in these models.

gr-qc↗

arXiv2007

Talking About Singularities

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 of the approaches to the general area and include discussions of the method of asymptotic splittings, singularity and completeness theorems and the use of the Bel-Robinson energy to prove completeness theorems and classify cosmological singularities.

gr-qc↗

arXiv2007

Flat, radiation universes with quadratic corrections and asymptotic analysis

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 provide solutions that are both regular initially and go over to Friedmann type at later times. We find here, by applying a dynamical systems approach, the general form of the solution to this class of models in the neighborhood of the initial singularity under the above conditions.

gr-qc↗

arXiv2007

Braneworld cosmological singularities

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.

gr-qc↗

arXiv2006

Cosmological Singularities and Bel-Robinson Energy

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 universes in conjunction with the Hubble expansion rate and the scale factor proves to be an appropriate measure leading to a complete classification of the possible singularities. We show how our scheme covers all known cases of cosmological asymptotics possible in these universes and also predicts new and distinct types of singularities. We further prove that various asymptotic forms met in flat cosmologies continue to hold true in their curved counterparts. These include phantom universes with their recently discovered big rips, sudden singularities as well as others belonging to graduated inflationary models.

gr-qc↗