What gives a "theory of Initial Conditions" ?

TL;DR

This paper reviews work on non-Hermitian Hamiltonians, highlighting their role in determining initial conditions and predicting cosmological features through effective equations of motion that resemble Hermitian systems over time.

Contribution

It demonstrates how non-Hermitian Hamiltonians can predict initial conditions and cosmological phenomena, bridging complex action theories with effective Hermitian dynamics.

Findings

Anti-Hermitian part determines solutions and initial conditions.

Effective equations become Hermitian-like after long times.

Cosmological predictions from saddle point behavior.

Abstract

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.