Decaying Vacuum Energy and Deflationary Cosmology in Open and Closed Universes

Abstract

We consider a nonsingular deflationary cosmological model with decaying vacuum energy density in universes of arbitrary spatial curvature. Irrespective of the value of $k$, the models are characterized by an arbitrary time scale $H_I^{-1}$ 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 $H_I^{-1}$ 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 $Λ_I/Λ_0 \simeq 10^{118}$ as theoretically suggested. It is also shown that all models allow a density parameter $Ω_0 <2/3$ and that the age of the universe is large enough to agree with observations even with the high value of $H_0$ suggested by recent measurements.