Evolution of the scale factor with a variable cosmological term
Abstract
The evolution of the scale factor $a(t)$ in Friedmann models (those with zero pressure and a constant cosmological term $\ensuremath{\Lambda})$ is well understood, and elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58, 689 (1986)]. Developments in particle physics and inflationary theory, however, increasingly indicate that $\ensuremath{\Lambda}$ ought to be treated as a dynamical quantity. We reexamine the evolution of the scale factor with a variable $\ensuremath{\Lambda}$ term, and also generalize the treatment to include nonzero pressure. New solutions are obtained and evaluated using a variety of observational criteria. Existing arguments for the inevitability of a big bang (i.e., an initial state with $a=0)$ are substantially weakened, and can be evaded in some cases with ${\ensuremath{\Lambda}}_{0}$ (the present value of $\ensuremath{\Lambda})$ well below current experimental limits.