QUANTUM INFLATIONARY MODEL AND THE UNCERTAINTY OF THE HUBBLE SIZE

A quantum inflationary universe model is proposed, in which the expansion factor S(t) is treated as a q-number, and the cosmological constant A is identified with the energy density of Higgs field. Moreover, the initial quantum state is assumed to be a Gauss wave pocket. In such framework, < S ^3/2> follows the classical de-Sitter expansive law. The relative quantum uncertainty of Hubble size l_H(t) = (S/S)^-1 was computed: Δl_H(t) / < l _H(t)>～Z^-6, where Z is the inflationary factor of universe. This result is basically different from that of Padmanabhan; the discrepency was explained. We conclude that the quantum Hubble size is practically a classical quantity.