Singularities in the dark energy universe are discussed, assuming that there is a bulk viscosity in the cosmic fluid. In particular, it is shown how the physically natural assumption of letting the bulk viscosity be proportional to the scalar expansion in a spatially flat FRW universe can drive the fluid into the phantom region (w < −1), even if it lies in the quintessence region (w > −1) in the non-viscous case.

Abstract.The solution of the dark energy problem in models without scalars is presented. It is shown that a late-time accelerating cosmology may be generated by an ideal fluid with some implicit equation of state. The evolution of the universe within modified GaussBonnet gravity is considered. It is demonstrated that such gravitational approach may predict the (quintessential, cosmological constant or transient phantom) acceleration of the late-time universe with a natural transition from deceleration to acceleration ( or from non-phantom to phantom era in the last case). ‡

In the case of a large class of static, spherically symmetric black hole solutions in higher order modified gravity models, an expression for the associated energy is proposed and identified with a quantity proportional to the constant of integration, which appears in the explicit solution. The identification is achieved making use of derivation of the First Law of black hole thermodynamics from the equations of motion, evaluating independently the entropy via Wald method and the Hawking temperature via quantum mechanical methods in curved space-times. Several non trivial examples are discussed, including a new topological higher derivative black hole solution, and the proposal is shown to work in all examples considered.

We discuss a modified form of gravity implying that the action contains a power α of the scalar curvature. Coupling with the cosmic fluid is assumed. As equation of state for the fluid, we take the simplest version where the pressure is proportional to the density. Based upon a natural ansatz for the time variation of the scale factor, we show that the equations of motion are satisfied for general α. Also the condition of conservation of energy and momentum is satisfied. Moreover, we investigate the case where the fluid is allowed to possess a bulk viscosity, and find the noteworthy fact that consistency of the formalism requires the bulk viscosity to be proportional to the power (2α − 1) of the scalar expansion. In Einstein's gravity, where α = 1, this means that the bulk viscosity is proportional to the scalar expansion. This mathematical result is of physical interest; as discussed recently by the present authors, there exists in principle a viscositydriven transition of the fluid from the quintessence region into the phantom region, implying a future Big Rip singularity.