Geodesic instability and isotropy of CMWBR

We give a detailed study of the various aspects of the mixing effects due to geodesic instability in compact negative curvature FLRW models, as an explicit function of the cosmological parameters and the topological compactification scale. Our results show that the effect is: (i) much less pronounced than some of the claims made previously; (ii) strongly dependent upon the current value of the cosmological density parameter . Nevertheless it can, for reasonable values of the density parameter, produce appreciable mixing with a consequent reduction in the measured CMWBR anisotropy on a range of angular scales. This effect is expressible in terms of the curvature scalar and is therefore gauge invariant. Furthermore, we show: (a) the usual observer area distance routinely employed in cosmological studies also encodes all the dynamical information relating to the geodesic instability; (b) the estimates of the length scales on the surface of the last scattering depend significantly on the density parameter, and could be significantly different in low density universes compared with a critical density universe.