Abstract
The intention of this paper is mainly two-fold. First, we point out a striking numerical agreement between the bulk viscosity in the lepton era calculated by Husdal (2016) and our own calculations of the present-day bulk viscosity when the functional form is ζ ∼ ρ . From a phenomenological point of view, we thus seem to have an ansatz for the viscosity, which bridges the infancy of the Universe (∼1 s) with the present. This can also be looked upon as a kind of symmetry between the early-time cosmology and the present-day cosmology: it is quite remarkable that the kinetic theory-based bulk viscosity in the early universe and the experimentally-based bulk viscosity in the present universe can be covered by the same simple analytical formula. Second, we consider the Kasner universe as a typical anisotropic model of Bianchi-Type I, investigating whether this geometrical model is compatible with constant viscosity coefficients in the fluid. Perhaps surprisingly, the existence of a shear viscosity turns out to be incompatible with the Kasner model. By contrast, a bulk viscosity is non-problematic in the isotropic version of the model. In the special case of a Zel’dovich (stiff) fluid, the three equal exponents in the Kasner metric are even determined by the bulk viscosity alone, independent of the value of the fluid energy density. We also give a brief comparison with some other recent approaches to viscous cosmology.
Highlights
Recent years have witnessed an increased interest in bulk-viscous properties in the cosmic fluid.From a hydrodynamicist’s point of view, it is almost surprising that this surge of interest has not occurred earlier
There are in general two viscosity coefficients, the shear viscosity η and the bulk viscosity ζ, corresponding to first-order deviation from thermal equilibrium, normally, the shear viscosity is omitted in cosmology because of the assumption about the spatial isotropy of the fluid
We present in this paper a striking similarity between the results obtained for the bulk viscosity of the late Universe [1] based on a much-used phenomenological approach (ζ ∼ ρ) and that calculated by Husdal and others for the early lepton era
Summary
Recent years have witnessed an increased interest in bulk-viscous properties in the cosmic fluid. We present in this paper a striking similarity between the results obtained for the bulk viscosity of the late Universe [1] based on a much-used phenomenological approach (ζ ∼ ρ) and that calculated by Husdal and others (see below) for the early lepton era. One might suspect that even a slight anisotropy in the cosmic fluid could compensate for the bulk viscosity. We consider this point, choosing the anisotropic Kasner universe as an example. The contributions include investigations of the early universe [13,14,15,16], the late universe [17,18,19], the phantom divide [20,21,22,23,24,25], models for the dark sector [26,27,28,29], and others [30,31,32,33,34,35,36,37,38,39]
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