We study the late-time evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type VII0 with a perfect fluid source. We show that, in contrast to models of Bianchi type VIIh which are asymptotically self-similar at late times, Bianchi VII0 models undergo a complicated type of self-similarity breaking. This symmetry breaking affects the late-time isotropization that occurs in these models in a significant way: if the equation of state parameter satisfies (4/3) the models isotropize as regards the shear but not as regards the Weyl curvature. Indeed, these models exhibit a new dynamical feature that we refer to as Weyl curvature dominance: the Weyl curvature dominates the dynamics at late times. By viewing the evolution from a dynamical systems perspective we show that, despite the special nature of the class of models under consideration, this behaviour has implications for more general models.

http://iopscience.iop.org/article/10.1088/0264-9381/16/8/302/pdf

Asymptotic self-similarity breaking at late times in cosmology

This review article is devoted to analyze the main properties characterizing the cosmological singularity associated to the homogeneous and inhomogeneous Mixmaster model. After the introduction of the main tools required to treat the cosmological issue, we review in details the main results got along the last forty years on the Mixmaster topic. We firstly assess the classical picture of the homogeneous chaotic cosmologies and, after a presentation of the canonical method for the quantization, we develop the quantum Mixmaster behavior. Finally, we extend both the classical and quantum features to the fully inhomogeneous case. Our survey analyzes the fundamental framework of the Mixmaster picture and completes it by accounting for recent and peculiar outstanding results.

Classical and Quantum Features of the Mixmaster Singularity

Our universe may have formed via bubble nucleation in an eternally-inflating background. Furthermore, the background may have a compact dimension — the modulus of which tunnels out of a metastable minimum during bubble nucleation — which subsequently grows to become one of our three large spatial dimensions. Then the reduced symmetry of the background is equivalent to anisotropic initial conditions in our bubble universe. We compute the inflationary spectrum in such a scenario and, as a first step toward understanding the effects of anisotropy, project it onto spherical harmonics. The resulting spectrum exhibits anomalous multipole correlations, their relative amplitude set by the present curvature parameter, which appear to extend to arbitrarily large multipole moments. This raises the possibility of future detection, if slow-roll inflation does not last too long within our bubble. A full understanding of the observational signal must account for the effects of background anisotropy on photon free streaming, and is left to future work.

Observable effects of anisotropic bubble nucleation

We study isotropization of the Universe by examining the evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type with dust or radiation as the source. By using expansion-normalized variables, which unlike the usual metric variables are bounded throughout the evolution, we are able to give complete numerical simulations of the models, from the Planck time to the far-distant future. We find that two types of intermediate isotropization, characterized by the shear being small relative to the rate of expansion, can occur in Bianchi cosmologies, leading to models which are potentially compatible with the highly isotropic cosmic microwave background observations. In the first type the density parameter is close to one, while in the second type, it is not necessarily close to one. We relate these results to discussions by Doroshkevich et al and by Barrow of how isotropization occurs in cosmology.

http://iopscience.iop.org/article/10.1088/0264-9381/15/2/008/pdf

On the isotropy of the Universe: do Bianchi cosmologies isotropize?

This paper reports a summary of the contents contents of six hours of lectures on the CMB anisotropy experiments given at the Strasbourg NATO school on the CMB and cosmology (Its companion paper, astro-ph/9705101 reports the lectures on the CMB spectrum) A context is set as a bridge from the theoretical CMB anisotropy lectures and the experimental situation The COBE DMR results are reveiwed in detail and as pioneer for future space missions Current and planned experiments are discussed in preference to reviewing already completed observations The NASA MidEX mission MAP is discussed in some detail including figures The ESA M3 mission Max Planck Surveyor is also reviewed in some detail though its final configuration is not yet fully settled The recent history and current versions are presented Tables and references for experiments are included

A. G. Doroshkevich

Papers

Primordial radiation in a homogeneous but anisotropic universe

Impossibility of mixing in a cosmological model of the Bianchi IX type.