Deflationary cosmology with decaying vacuum energy density

Abstract

A nonsingular cosmological scenario based on a new phenomenological decay law for the effective $\ensuremath{\Lambda}$ term is proposed. In such a model, the cosmic history began from an instability of the de Sitter space-time rather than a singularity. The process is characterized by an arbitrary time scale ${H}_{I}^{\ensuremath{-}1}$ giving the largest value of the cosmological constant (${\ensuremath{\Lambda}}_{I}={3H}_{I}^{2}$) and the initial temperature of the Universe. Subsequently, the Universe evolved continuously toward a slightly modified Friedmann-Robertson-Walker cosmology. Among the "remnants" of the primordial inflationary period are the present values of the cosmological term ${\ensuremath{\Lambda}}_{0}\ensuremath{\sim}3\ensuremath{\beta}{H}_{0}^{2}$, the density parameter ${\ensuremath{\Omega}}_{0}\ensuremath{\sim}1\ensuremath{-}\ensuremath{\beta}$, and the deceleration parameter $\frac{{q}_{0}\ensuremath{\sim}(1\ensuremath{-}3\ensuremath{\beta})}{2}$, where $\ensuremath{\beta}$ is smaller than unity. In addition, the age parameter of the vacuum-matter-dominated phase is ${H}_{0}{t}_{0}\ensuremath{\sim}\frac{2}{3}(1\ensuremath{-}\ensuremath{\beta})$. It is also shown that, if ${H}_{I}^{\ensuremath{-}1}$ is of the order of the Planck time, the Universe started with the Planck temperature and this model is consistent with the theoretically suggested value $\frac{{\ensuremath{\Lambda}}_{1}}{{\ensuremath{\Lambda}}_{0}\ensuremath{\sim}{10}^{118}}$.