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

What gives a "theory of Initial Conditions" ?