  The present work contains a review of some of the work we have done on
complex action or non-Hermitian Hamiltonian theory, especially the result that
the anti-Hermitian part of the Hamiltonian functions by determining the actual
solution to the equations of motion, that should be realized; this means it
predicts the initial conditions. It should be stressed that a major result of
ours is that the effective equations of motion will in practice -- after long
time -- be so accurately as if we had indeed a Hermitian Hamiltonian, and so
there is at first nothing wrong in assuming a non-Hermitian one. In fact it
would practically seem Hermitian anyway! A major new point is that we seek by a
bit intuitively arguing to suggest some cosmologically predictions from the
mentioned initial conditions predicted: We seek even by assumming essentially
nothing but very general properties of the non-Hermitian Hamiltonian that we in
practice should find a bottom in the (effective Hermitian) Hamiltonian and that
the Universe at some moment should pass through a (multiple) saddle point very
closely, so that the time spent at it would be very long.
