The Evolution of Anisotropy in Nonrotating Bianchi Type V Cosmologies

Abstract

view Abstract Citations (44) References (5) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Evolution of Anisotropy in Nonrotating Bianchi Type V Cosmologies Matzner, Richard A. Abstract We consider the effect of neutrino viscosity and of free neutrinos in universes of Bianchi types I and V. We discuss the collisionless Boltzmann equation (which gives the evolution of the neutrino-distribu~ tion function) for these types and compare the type V results with those for type I previously given by Misner. \7tje assume that dissipative effects lower pa/p (the ratio of the anisotropy energy density to the matter energy density, both measured by their gravitational effect on the expansion) to a number of order unity before the electron neutrinos become collisionless. We are unable to integrate the null geodesics completely in type V, so we are unable to present a complete numerical example of the dynamics of the model with collisionless radiation. We do, however, present an approximate model universe of type V which begins its free evolution with p~ = p at a tem- perature of `-~-`1O'° ° K. The approximation lies in an assumption of small j3 for the subsequent motion (where j3 is a parameter describing the anisotropy). This model predicts L~.T/T `-~` 2 X 1O-~ for the varia- tion in the primordial radiation temperature, if one assumes a switchover from radiation domination to matter domination at T `-S-' 3000 K. This variation L~T/T is of the same order as that found previously for type I and type IX by Misner. There is, however, a new feature, since there is an asymmetry (in the strength of the anisotropy) between opposite hemispheres. Depending on the current relative sizes of p~ (the matter density) and R* (the 3-space curvature), this asymmetry can be quite strong. An estimate taking parameters consistent with current observations suggests an excess of < 5-10 in the amplitude of the anisotropy in the hemisphere 0> ir/2, compared with the hemisphere 8 <ir/2, for the epoch when p~1 R* `~ 1. (The current epoch has Pm1 R* <1. Publication: The Astrophysical Journal Pub Date: September 1969 DOI: 10.1086/150138 Bibcode: 1969ApJ...157.1085M full text sources ADS |