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We study cosmological models derived from higher-order Gauss-Bonnet gravity $F(R,G)$ by using the Lagrange multiplier approach without assuming the presence of additional fields with the exception of standard perfect fluid matter. The presence of Lagrange multipliers reduces the number of allowed solutions. We need to introduce compatibility conditions of the FRW equations, which impose strict restrictions on the metric or require the introduction of additional exotic matter. Several classes of $F(R,G)$ models are generated and discussed., Comment: 8 pages, to appear in Astro. Space Sci

We study higher--order variational derivatives of a generic second--order Lagrangian ${\cal L}={\cal L}(x,\phi,\partial\phi,\partial^2\phi)$ and in this context we discuss the Jacobi equation ensuing from the second variation of the action. We exhibit the different integrations by parts which may be performed to obtain the Jacobi equation and we show that there is a particular integration by parts which is invariant. We introduce two new Lagrangians, ${\cal L}_1$ and ${\cal L}_2$, associated to the first and second--order deformations of the original Lagrangian ${\cal L}_0$ respectively; they are in fact the first elements of a whole hierarchy of Lagrangians derived from ${\cal L}_0$. In terms of these Lagrangians we are able to establish simple relations between the variational derivatives of different orders of a given Lagrangian. We then show that the Jacobi equations of ${\cal L}_0$ may be obtained as variational equations, so that the Euler--Lagrange and the Jacobi equations are obtained from a single variational principle based on the first--order variation ${\cal L}_1$ of the Lagrangian. We can furthermore introduce an associated energy--momentum tensor ${{\cal H}^\mu}_\nu$ which turns out to be a conserved quantity if ${\cal L}_0$ is independent of space--time variables., Comment: This article was originally published in Differential Geometry and Applications, Proc. Conf., Aug. 28 - Sept. 1, 1995, Brno, Czech Republic (Masaryk University, Brno, 1996), pp. 353-372. Since it is hardly available we post it here for the interested audience

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation., Comment: 21 pages, LaTeX file, no figures. Replaced version to be published on Phys. Rev. D

The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account to gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle gravitational and matter degrees of freedom (passing from the Jordan frame to the Einstein frame) but they acquire a physical meaning considering the bi-metric structure of Palatini approach which allows to distinguish between spacetime structure and geodesic structure. Examples of higher-order and non-minimally coupled theories are worked out and relevant cosmological solutions in Einstein frame and Jordan frames are discussed showing that also the interpretation of cosmological observations can drastically change depending on the adopted frame.

The evidence of the acceleration of universe at present time has lead to investigate modified theories of gravity and alternative theories of gravity, which are able to explain acceleration from a theoretical viewpoint without the need of introducing dark energy. In this paper we study alternative gravitational theories defined by Lagrangians which depend on general functions of the Ricci scalar invariant in minimal interaction with matter, in view of their possible cosmological applications. Structural equations for the spacetimes described by such theories are solved and the corresponding field equations are investigated in the Palatini formalism, which prevents instability problems. Particular examples of these theories are also shown to provide, under suitable hypotheses, a coherent theoretical explanation of earlier results concerning the present acceleration of the universe and cosmological inflation. We suggest moreover a new possible Lagrangian, depending on the inverse of sinh(R), which gives an explanation to the present acceleration of the universe., Comment: 23 pages, Revtex4 file

We criticize and generalize some properties of Noether charges presented in a paper by V. Iyer and R. M. Wald and their application to entropy of black holes. The first law of black holes thermodynamics is proven for any gauge-natural field theory. As an application charged Kerr-Newman solutions are considered. As a further example we consider a (1+2) black hole solution.

We apply a global and geometrically well-defined formalism for spinor-dilaton-gravity to two-dimensional manifolds. We discuss the general formalism and focus attention on some particular choices of the dilatonic potential. For constant dilatonic potential the model turns out to be completely solvable and the general solution is found. For linear and exponential dilatonic potentials we present the class of exact solutions with a Killing vector., Comment: 21 pages, LaTeX, minor changes in text and format, final version to appear in Classical and Quantum Gravity