Abstract
In paper the closed Friedmann-Robertson-Walker model with quantization in presence of the positive cosmological constant, radiation and Chaplygin gas is studied. For analysis of tunneling probability for birth of an asymptotically deSitter, inflationary Universe as a function of the radiation energy a new definition of a "free" wave propagating inside strong fields is introduced. Vilenkin's tunneling boundary condition is corrected, penetrability and reflection are calculated in fully quantum stationary approach.
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