INSTABILITY OF THE ONE-TEXTURE UNIVERSE

The one-texture universe, introduced by Davis in 1987, is a homogeneou s mapping of a scalar field with an S-3 vacuum into a closed universe. It has long been known to mathematicians that such solutions, althoug h static, are unstable. We show by explicit construction that there ar e four degenerate lowest modes which are unstable, corresponding to co llapse of the texture towards a single point, in the case where gravit ational back reaction is neglected. We discuss the instability time sc ale 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 c osmic microwave background constrains the initial magnitude of this un stable perturbation to be less than similar to 10(-3).