On a closure hypothesis in the theory of cosmic turbulence

The problem how to introduce an extended version of Heisenberg's closure hypothesis in the theory of cosmic turbulence is expounded. To be definite, the requirements are as follows: the hypothesis is applied only in the physically relevant frame; in this frame, the physical wave-number of the biggest eddy is identified with the reciprocal of the length specifying the event horizon; in the limit when the cosmic expansion disappears, the hypothesis is automatically reduced to the usual Heisenberg one. An isotropic big-bang universe is considered whose cosmic expansion is specified by an expansion parameter and whose inertial mass density is a definite cosmic time function. (Mori, K.)