Abstract:We derive a general formalism for bulk viscous solutions of the energy-conservation equation for ρ(a, ζ), both for a single-component and a multicomponent fluid in the Friedmann universe. For our purposes, these general solutions become valuable in estimating the order of magnitude of the phenomenological viscosity in the cosmic fluid at present. H(z) observations are found to put an upper limit on the magnitude of the modulus of the present-day bulk viscosity. It is found to be ζ 0 ∼ 10 6 Pa·s, in agreement with previous works. We point out that this magnitude is acceptable from a hydrodynamic point of view. Finally, we bring new insight by using our estimates of ζ to analyze the fate of the future universe. Of special interest is the case ζ ∝ √ ρ for which the fluid, originally situated in the quintessence region, may slide through the phantom barrier and inevitably be driven into a big rip. Typical rip times are found to be a few hundred Gy.Keywords: viscous cosmology; bulk viscosity; big rip; fate of the universe PACS: 98.80.Jk; 95.35.+d; 95.36.+x

In this paper the dynamics of free gauge fields in Bianchi type I–VIIh space-times is investigated. The general equations for a matter sector consisting of a p-form field strength (), a cosmological constant (4-form) and perfect fluid in Bianchi type I–VIIh space-times are computed using the orthonormal frame method. The number of independent components of a p-form in all Bianchi types I–IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions, ‘Wonderland (λ)’ appears generally in type V and in type I for . Depending on the value of the equation of state parameter other new stable solutions are also found (‘The Rope’ and ‘The Edge’) containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.

We analyze characteristic properties of two different cosmological models: (i) a one-component dark energy model where the bulk viscosity ζ is associated with the fluid as a whole, and (ii) a two-component model where ζ is associated with a dark matter component ρm only, the dark energy component considered inviscid. Shear viscosity is omitted. We assume throughout the simple equation of state p = wρ, with w a constant. In the one-component model we consider two possibilities, either to take ζ proportional to the scalar expansion (equivalent to the Hubble parameter), in which case the evolution becomes critically dependent on the value of the small constant α = 1 + w and the magnitude of ζ. Second, we consider the case ζ = const., where a de Sitter final stage is reached in the future. In the two-component model we consider only the case where the dark matter viscosity ζm is proportional to the square of ρm, where again a de Sitter form is found in the future. In this latter case the formalism is supplemented by a phase space analysis. As a general result of our considerations we suggest that a value ζ0 ∼ 10 6 Pa s for the present viscosity is reasonable, and that the two-component model seems to be favored. 95.36.+x

We investigate a corner of the Bianchi models that has not received much attention: "extended FLRW models" (eFLRW) defined as a cosmological model with underlying anisotropic Bianchi geometry that nevertheless expands isotropically and can be mapped onto a reference FLRW model with the same expansion history. In order to investigate the stability and naturalness of such models in a dynamical systems context, we consider spatially homogeneous models that contain a massless scalar field ϕ and a non-tilted perfect fluid obeying an equation of state p = wρ. Remarkably, we find that matter anisotropies and geometrical anisotropies tend to cancel out dynamically. Hence, the expansion is asymptotically isotropic under rather general conditions. Although extended FLRW models require a special matter sector with anisotropies that are "fine-tuned" relative to geometrical anisotropies, our analysis shows that such solutions are dynamically preferred attractors in general relativity. Specifically, we prove that all locally rotationally symmetric Bianchi type III universes with space-like ∇ µ ϕ are asymptotically shear-free, for all w ∈ [−1, 1]. Moreover, all shear-free equilibrium sets with anisotropic spatial curvature are proved to be stable with respect to all homogeneous perturbations for w ≥ −1/3.1 The origin of these features is still unclear and there is an ongoing discussion if they are indicating new physics or if they are merely statistical fluctuations. See [9] for a discussion on possible implications of the tension related to the lensing amplitude, with CMB spectra favoring a positive spatial curvature at more than the 99% confidence level. For reviews on the socalled "ΛCDM anomalies", see [10][11][12] and references therein.2 In its simplest version, the cosmological principle should also postulate the Universe's spatial topology [15]. Usually, and this is the case here, this is taken to be the trivial topology.

Continuing previous work, we show the existence of stable, anisotropic future attractors in Bianchi invariant sets with a p-form field (p ∈ {1, 3}) and a perfect fluid. In particular, we consider the not previously investigated Bianchi invariant sets B(II), B(IV), B(VII 0 ) and B(VII h ) and determine their asymptotic behaviour. We find that the isolated equilibrium set Wonderland is a future attractor on all of its existence (2/3 < γ < 2) in all these sets except in B(II), where the peculiar equilibrium sets Edge and Rope show up, taking over the stability for certain values of γ. In addition, in B(IV) and B(VII h ) plane gravitational wave solutions (with a non-zero p-form) serve as attractors whenever 2/3 < γ < 2.