Abstract
We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropization on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialize to consider the closed Bianchi type IX universe, and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate on approach to the singularity, it will be anisotropic. We include an isotropic ultra-stiff ghost fluid with negative energy density in order to create a cosmological bounce at finite volume in the absence of the anisotropic fluid. When the dominant anisotropic fluid is present it leads to an anisotropic cosmological singularity rather than an isotropic bounce. The inclusion of anisotropic stresses generated by collisionless particles in an anisotropically expanding universe is therefore essential for a full analysis of the consequences of a cosmological bounce or singularity in cyclic universes.
Highlights
The standard model of cosmology has been subjected to detailed scrutiny by recent WMAP and Planck mission data
There are several types of anisotropy that need to be investigated in order to ascertain the viability of cyclic cosmologies: simple expansion rate anisotropy, spatial curvature anisotropy, and pressure anisotropy
We have focussed on the effects of pressure anisotropies in simple ekpyrotic [14, 25, 35] cyclic universe scenarios that are more general and complicated than those first studied by Barrow and Yamamoto [18]
Summary
The standard model of cosmology has been subjected to detailed scrutiny by recent WMAP and Planck mission data. The need to include anisotropic pressures on approach to the singularity is important because interactions all become collisionless at a higher temperature in the case of anisotropic expansion, than in the isotropic case Their interaction rates can be written as G = snv ~ ga2T , where σ is the interaction cross section, n is the number density of particles, v is the average velocity of the particles, α is the generalized structure constant associated with any interaction mediated by some gauge boson, T is the temperature of the universe and g is the effective number of relativistic degrees of freedom of particles at the.
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