On the instability of the one-texture universe

Abstract

The one-texture universe, introduced by Davis in 1987, is a homogeneous mapping of a scalar field with an $S^3$ vacuum into a closed universe. It has long been known to mathematicians that such solutions, although static, are unstable. We show by explicit construction that there is only one unstable mode, corresponding to collapse of the texture towards a single point, in the case where gravitational backreaction is neglected. We discuss the instability timescale in both static and expanding space-times; in the latter case it is of order of the present age of the universe, suggesting that, though unstable, the one-texture universe could survive to the present. The cosmic microwave background constrains the initial magnitude of this unstable perturbation to be less than of order 10^{-3}.