Two-scalar model for a small but nonzero cosmological constant

Abstract

We reexamine a model of the two-scalar system proposed previously for understanding a small but nonzero cosmological constant. The model provides solutions of the scalar-field energy ${\ensuremath{\rho}}_{s}$ which behaves as a true constant for a limited time interval rather than in the way of tracker- or scaling-type variations. This causes mini-inflation, as indicated by recent observations. As another novel feature, ${\ensuremath{\rho}}_{s}$ and the ordinary matter density ${\ensuremath{\rho}}_{m}$ always fall off side by side, but interlacing, also as $(\mathrm{time}{)}^{\ensuremath{-}2}$ as an overall behavior in conformity with the scenario of a decaying cosmological constant. Mini-inflation occurs whenever ${\ensuremath{\rho}}_{s}$ overtakes ${\ensuremath{\rho}}_{m},$ which may happen more than once, shedding new light on the coincidence problem. We present a new example of the solution, and offer an intuitive interpretation of the mechanism of the nonlinear dynamics. We also discuss the chaoslike nature of the solution.