Singularities of varying light speed cosmologies

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 dimensional systems which are then analyzed both by dynamical systems techniques in phase space and by applying the method of asymptotic splittings. In the general case we find initially expanding closed models which recollapse to a future singularity and open universes that are eternally expanding towards the future. The precise nature of the singularities is also discussed.Comment: 7 pages, 2 figures, uses iop style files, to appear in the Proceedings of the Greek Relativity Meeting NEB12, June 29-July 2, 2006, Nauplia, Greec

Slice Energy and Theories of Gravitation

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 component and the scalar field generated by the conformal transformation to the Einstein frame of such theories and the issue of the physical equivalence of different conformal frame representations. We show that all such conformally-related, generalized theories of gravitation allow for the slice energy to be invariably defined and its fundamental properties be insensitive to conformal transformations.Comment: 16 pages, In: Proceedings of the 11th Greek Relativity Meetin

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.Comment: 18 pages, references added, remark added in last Section related to the choice of physical frame, various other improvements, final version to appear in Gravitation and Cosmolog

Geodesics at Sudden Singularities

We show that a general solution of the Einstein equations that describes approach to an inhomogeneous and anisotropic sudden spacetime singularity does not experience geodesic incompleteness. This generalises the result established for isotropic and homogeneous universes. Further discussion of the weakness of the singularity is also included.Comment: v2: 7 pages, minor improvements, version to appear in PR

Brane singularities and their avoidance

The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, 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. In the case where the bulk field content is parametrized by an analogue of perfect fluid with an arbitrary equation of state P=\gamma\rho between the `pressure' P and the `density' \rho, our results depend crucially on the constant fluid parameter \gamma: (i) For \gamma>-1/2, the flat brane solution suffers from a collapse singularity at finite distance, that disappears in the curved case. (ii) For \gamma<-1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For -1<\gamma< or = -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.Comment: 37 pages, latex, merged version of arXiv:1005.3221 and arXiv:1004.3379, to appear in Class.Quant.Gra

Variational and conformal structure of nonlinear metric-connection gravitational lagrangians

We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first order formalism when applied to these theories may lead consistently to a new method of reduction of order of the associated field equations. We show that the similarity of the field equations which are derived from appropriate actions via this formalism to those produced by Hilbert varying purely metric Lagrangians is not merely formal but is implied by the diffeomorphism covariant property of the associated Lagrangians. We prove that the conformal equivalence theorem of these theories with general relativity plus a scalar field, holds in the extended framework of Weyl geometry with the same forms of field and self-interacting potential but, in addition, there is a new `source term' which plays the role of a stress. We point out how these results may be further exploited and address a number of new issues that arise from this analysis.Comment: 8 pages, LaTeX (REVTeX 3.1), submitted to J. Math. Phys., references added (nothing changed but LaTeX style

Series expansions and sudden singularities

We construct solutions of the Friedmann equations near a sudden singularity using generalized series expansions for the scale factor, the density, and the pressure of the fluid content. In this way, we are able to arrive at a solution with a sudden singularity containing two free constants, as required for a general solution of the cosmological equations.Comment: 4 pages, contribution for the Proceedings of the MG13 Meeting on General Relativity, Stockholm, July 201

Comment to the paper `Conformal transformations single out a unique measure of distance'

We discuss the consequences of the incorrectness [see the Erratum in Phys. Rev D 49, 1145 (1994)] of that paper and add two related remarks. The scope of this comment is to encourage further research on: `Which of the conformally equivalent metrics is the physical one?'Comment: 4 pages, LaTeX, published in Phys. Rev. D52, 6198 (1995