Mathematics Colloquia and Seminars

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In joint work with Blake Temple, we show the instability in the flat p = 0 Friedmann spacetime in the class of solutions that are smooth at the centre of symmetry. Within this class there exists a subclass of expanding solutions, denoted by F, that decay time asymptotically to k<0 Friedmann spacetimes. We prove that F is represented by the domain of attraction of a stable rest point M at every order of expansion in the self-similar variable xi = r/t about the fixed point SM, which represents the k=0 Friedmann spacetime. Generically, solutions in F diverge from k<0 Friedmann spacetimes at intermediate times, and return to them at late times, making F a natural extension of the k<0 Friedmann spacetimes. Most interestingly, these divergences exhibit accelerations despite the absence of a cosmological constant.