Time-symmetric quantum cosmology and our Universe

The author investigates the time neutral formulation of quantum cosmology of Gell-Mann and Hartle (1992). In particular he studies the proposal discussed by them that the Universe corresponds to the time-symmetric decoherence functional with an initial and final density matrix of low entropy. He shows that the Universe does not correspond to this time-symmetric 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.