Superspace and global stability in General Relativity
  A framework is developed enabling the global analysis of the stability of
cosmological models using the local geometric characteristics of the
infinite-dimensional superspace, i.e. using the generalised Jacobi equation
reformulated for pseudo-Riemannian manifolds. We give a direct formalism for
dynamical analysis in the superspace, the requisite equation pertinent for
stability analysis of the universe by means of generalized covariant and Fermi
derivative is derived. Then, the relevant definitions and formulae are
retrieved for cosmological models with a scalar field.
