  We investigate the time neutral formulation of quantum cosmology of Gell-Mann
and Hartle. In particular we study the proposal discussed by them that our
Universe corresponds to the time symmetric decoherence functional with initial
and final density matrix of low entropy. We show that our Universe does not
correspond to this proposal by investigating the behaviour of small
inhomogeneous perturbations around a Friedman-Robertson-Walker model. These
perturbations cannot be time symmetric if they were small at the Big Bang.
