Hyperextended Scalar-Tensor Gravity

We study a general Scalar-Tensor Theory with an arbitrary coupling funtion $\omega (\phi )$ but also an arbitrary dependence of the ``gravitational constant'' $G(\phi )$ in the cases in which either one of them, or both, do not admit an analytical inverse, as in the hyperextended inflationary scenario. We present the full set of field equations and study their cosmological behavior. We show that different scalar-tensor theories can be grouped in classes with the same solution for the scalar field.Comment: latex file, To appear in Physical Review

Some exact non-vacuum Bianchi VI0 and VII0 instantons

We report some new exact instantons in general relativity. These solutions are K\"ahler and fall into the symmetry classes of Bianchi types VI0 and VII0, with matter content of a stiff fluid. The qualitative behaviour of the solutions is presented, and we compare it to the known results of the corresponding self-dual Bianchi solutions. We also give axisymmetric Bianchi VII0 solutions with an electromagnetic field.Comment: latex, 15 pages with 3 eps figure

Non-Vacuum Bianchi Types I and V in f(R) Gravity

In a recent paper \cite{1}, we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f(R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.Comment: 15 pages, accepted for publication in Gen. Realtiv. Gravi

The conformal status of ω=−3/2\omega=-3/2 Brans-Dicke cosmology

Following recent fit of supernovae data to Brans-Dicke theory which favours the model with $\omega = - 3/2$ \cite{fabris} we discuss the status of this special case of Brans-Dicke cosmology in both isotropic and anisotropic framework. It emerges that the limit $\omega = -3/2$ is consistent only with the vacuum field equations and it makes such a Brans-Dicke theory conformally invariant. Then it is an example of the conformal relativity theory which allows the invariance with respect to conformal transformations of the metric. Besides, Brans-Dicke theory with $\omega = -3/2$ gives a border between a standard scalar field model and a ghost/phantom model. In this paper we show that in $\omega = -3/2$ Brans-Dicke theory, i.e., in the conformal relativity there are no isotropic Friedmann solutions of non-zero spatial curvature except for $k=-1$ case. Further we show that this $k=-1$ case, after the conformal transformation into the Einstein frame, is just the Milne universe and, as such, it is equivalent to Minkowski spacetime. It generally means that only flat models are fully consistent with the field equations. On the other hand, it is shown explicitly that the anisotropic non-zero spatial curvature models of Kantowski-Sachs type are admissible in $\omega = -3/2$ Brans-Dicke theory. It then seems that an additional scale factor which appears in anisotropic models gives an extra deegre of freedom and makes it less restrictive than in an isotropic Friedmann case.Comment: REVTEX4, 19 pages, 8 figures, references adde

Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1

In this paper we classify all 4+1 cosmological models where the spatial hypersurfaces are connected and simply connected homogeneous Riemannian manifolds. These models come in two categories, multiply transitive and simply transitive models. There are in all five different multiply transitive models which cannot be considered as a special case of a simply transitive model. The classification of simply transitive models, relies heavily upon the classification of the four dimensional (real) Lie algebras. For the orthogonal case, we derive all the equations of motion and give some examples of exact solutions. Also the problem of how these models can be compactified in context with the Kaluza-Klein mechanism, is addressed.Comment: 24 pages, no figures; Refs added, typos corrected. To appear in CQ

Isotropization of Bianchi-Type Cosmological Solutions in Brans-Dicke Theory

The cosmic, general analitic solutions of the Brans--Dicke Theory for the flat space of homogeneous and isotropic models containing perfect, barotropic, fluids are seen to belong to a wider class of solutions --which includes cosmological models with the open and the closed spaces of the Friedmann--Robertson--Walker metric, as well as solutions for models with homogeneous but anisotropic spaces corresponding to the Bianchi--Type metric clasification-- when all these solutions are expressed in terms of reduced variables. The existence of such a class lies in the fact that the scalar field, $\phi$, times a function of the mean scale factor or ``volume element'', $a^3 = a_1 a_2 a_3$, which depends on time and on the barotropic index of the equation of state used, can be written as a function of a ``cosmic time'' reduced in terms of another function of the mean scale factor depending itself again on the barotropic index but independent of the metrics here employed. This reduction procedure permites one to analyze if explicitly given anisotropic cosmological solutions ``isotropize'' in the course of their time evolution. For if so can happen, it could be claimed that there exists a subclass of solutions that is stable under anisotropic perturbations.Comment: 15 pages, Late

Orientifolds and Slumps in G_2 and Spin(7) Metrics

We discuss some new metrics of special holonomy, and their roles in string theory and M-theory. First we consider Spin(7) metrics denoted by C_8, which are complete on a complex line bundle over CP^3. The principal orbits are S^7, described as a triaxially squashed S^3 bundle over S^4. The behaviour in the S^3 directions is similar to that in the Atiyah-Hitchin metric, and we show how this leads to an M-theory interpretation with orientifold D6-branes wrapped over S^4. We then consider new G_2 metrics which we denote by C_7, which are complete on an R^2 bundle over T^{1,1}, with principal orbits that are S^3\times S^3. We study the C_7 metrics using numerical methods, and we find that they have the remarkable property of admitting a U(1) Killing vector whose length is nowhere zero or infinite. This allows one to make an everywhere non-singular reduction of an M-theory solution to give a solution of the type IIA theory. The solution has two non-trivial S^2 cycles, and both carry magnetic charge with respect to the R-R vector field. We also discuss some four-dimensional hyper-Kahler metrics described recently by Cherkis and Kapustin, following earlier work by Kronheimer. We show that in certain cases these metrics, whose explicit form is known only asymptotically, can be related to metrics characterised by solutions of the su(\infty) Toda equation, which can provide a way of studying their interior structure.Comment: Latex, 45 pages; minor correction

Bianchi type II,III and V diagonal Einstein metrics re-visited

We present, for both minkowskian and euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for minkowskian signature elliptic functions are essential in the metric while for euclidean signature only elementary functions appear

Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation

The D-dimensional cosmological model on the manifold $M = R \times M_{1} \times M_{2}$ describing the evolution of 2 Einsteinian factor spaces, $M_1$ and $M_2$, in the presence of multicomponent perfect fluid source is considered. The barotropic equation of state for mass-energy densities and the pressures of the components is assumed in each space. When the number of the non Ricci-flat factor spaces and the number of the perfect fluid components are both equal to 2, the Einstein equations for the model are reduced to the generalized Emden-Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin within discrete-group analysis. Using the integrable classes of this equation one generates the integrable cosmological models. The corresponding metrics are presented. The method is demonstrated for the special model with Ricci-flat spaces $M_1,M_2$ and the 2-component perfect fluid source.Comment: LaTeX file, no figure

Further results on non-diagonal Bianchi type III vacuum metrics

We present the derivation, for these vacuum metrics, of the Painlev\'e VI equation first obtained by Christodoulakis and Terzis, from the field equations for both minkowskian and euclidean signatures. This allows a complete discussion and the precise connection with some old results due to Kinnersley. The hyperk\"ahler metrics are shown to belong to the Multi-Centre class and for the cases exhibiting an integrable geodesic flow the relevant Killing tensors are given. We conclude by the proof that for the Bianchi B family, excluding type III, there are no hyperk\"ahler metrics.Comment: 21 pages, no figure