From de sitter to de sitter: a non-singular inflationary universe driven by vacuum

Abstract

A semi-classical analysis of vacuum energy in the expanding space–time suggests that the cosmological term decays with time, with a concomitant matter production. For early times we find, in Planck units, Λ ≈ H4, where H is the Hubble parameter. The corresponding cosmological solution has no initial singularity, existing since an infinite past. During an infinitely long period we have a quasi-de Sitter, inflationary universe, with H ≈ 1. However, at a given time, the expansion undertakes a phase transition, with H and Λ decreasing to nearly zero in a few Planck times, producing a huge amount of radiation. On the other hand, the late-time scenario is similar to the standard model, with the radiation phase followed by a dust era, which tends asymptotically to a de Sitter universe, with vacuum dominating again.