On the creation of scalar particles in an early stage of the Friedmann closed-universe

Under impetus of the two experimental studies on neutrinos by Reines-group and Lyubimov's, it has been shown by Zel'dovich et al. that the cosmological universe is closed, provided that the neutrino masses m sub(νi) (i = e, μ, tau) satisfy the inequality Σsub(i)m sub(νi)c2 >= 20 eV. In a previous paper, the senior author dealt with the creation of scalar particles in an expanding universe with non-flat 3-space, but the case of a closed universe was practically ignored owing to the situation that the positive frequency part (in the sense of the author) of a quantized scalar field is not well-defined in that universe. In view of these circumstances, the creation of scalar particles in an early stage of the Friedmann closed-universe is studied on the supposition that the Fulling condition is preferable to define the positive frequency part in question near the early stage (as well as the later one). (author)