Decaying vacuum energy and deflationary cosmology in open and closed universes.

We consider a nonsingular deflationary cosmological model with a decaying vacuum energy density in universes of arbitrary spatial curvature. Irrespective of the value of {ital k}, the models are characterized by an arbitrary time scale {ital H}{sup {minus}1}{sub {ital I}} which determines the initial temperature of the universe and the largest value of the vacuum energy density, the slow decay of which generates all the presently observed matter energy of the Universe. If {ital H}{sup {minus}1}{sub {ital I}} is of the order of the Planck time, the models begin with the Planck temperature and the present day value of the cosmological constant satisfies {Lambda}{sub {ital I}}/{Lambda}{sub 0}{approx_equal}10{sup 118} as theoretically suggested. It is also shown that all models allow a density parameter {Omega}{sub 0}{lt}2/3 and that the age of the Universe is large enough to agree with observations even with the high value of {ital H}{sub 0} suggested by recent measurements. {copyright} {ital 1996 The American Physical Society.}