Mathematical structure of quantum superspace as a consequence of time asymmetry

It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace of the wave functions of the universe, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields directly an irreversible evolution, in the classical (and semiclassical) phase of the universe, where decoherence and correlations take place and therefore give origin to a classical universe, the second law of thermodynamics is demonstrated, connection with the Reichenbach branch system idea can be implemented, some rough coincidences with observational data are obtained, the arrows of time can be correlated, and time asymmetry can be explained as a state space asymmetry (e.g., like a spontaneous symmetry breaking). All these facts solve the problem of time asymmetry and show that it is time asymmetry itself that defines the most important features of the mathematical structure of superspace.