Time reversal symmetry in cosmology and the quantum creation of universes
The classical evolution of the universe can be seen as a parametrised worldline of the minisuperspace, with the time variable $t$ being the parameter that parametrises the worldline. The time reversal symmetry of the classical action implies then that for any positive oriented solution it must be a symmetric negative oriented one that, in terms of the same time variable, represent an expanding and a contracting universe, respectively. However, the choice of the time variable induced by the correct value of the Schrodinger equation in the two universes makes that their physical time variables are reversely related. Thus, the two universes turn out to be expanding universes from the point of view of their internal inhabitants, who identify matter with the particles that move in their spacetimes and antimatter with the particles that move in the symmetric universe. This might explain two of the main problems in cosmology: the time asymmetry observed in the context of a single universe and the matter-antimatter asymmetry of the primordial universe.