Expanding universes in the conformal frame of f(R)f(R) gravity

The late time evolution of Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source is studied in the conformal frame of $f(R)$ gravity. We assume that the corresponding scalar field, nonminimally coupled to matter, has an arbitrary non-negative potential function $V(\phi)$. We prove that equilibria corresponding to non-negative local minima for $V$ are asymptotically stable. We investigate all cases where one of the matter components eventually dominates. The results are valid for a large class of non-negative potentials without any particular assumptions about the behavior of the potential at infinity. In particular for a nondegenerate minimum of the potential with zero critical value we show that if $\gamma$, the parameter of the equation of state is larger than one, then there is a transfer of energy from the fluid to the scalar field and the later eventually dominates.Comment: Talk given in "The Invisible Universe", June 29 - July 3, 2009, Pari

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

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