Decoherence and back reaction: The origin of the semiclassical Einstein equations

Two basic properties defining classical behavior are "decoherence" and "correlations between co-ordinates and momenta." We study how the correlations that define the semiclassical decohering histories of the relevant cosmological variables are affected by the interaction with an environment formed by unobserved ("irrelevant") degrees of freedom. For some quantum cosmological models we analyze under what conditions the semiclassical coarse-grained histories obey the so-called semiclassical Einstein's equations (i.e., $G_{\mu \nu }=\kappa 〈T_{\mu \nu }〉$). These equations are shown to be valid only as a description of adiabatic regions of histories for which the interference effects have been suppressed. We also discuss the problem related to the existence of divergences in the decoherence factor of various quantum cosmological models.