Quintessence and the Transition to an Accelerating Universe
  The implications of seven popular models of quintessence based on supergravity or M/string theory for the transition from a decelerating to an accelerating universe are explored. All seven potentials can mimic the LambdaCDM model at low redshifts 0 < z < 5. However, for a natural range of initial values of the quintessence field, the SUGRA and Polonyi potentials predict a transition redshift z_t = 0.5 for Omega_Lambda0 = 0.70, in agreement with the observational value z_t = 0.46 and in mild conflict with the LambdaCDM value z_t = 0.67. Tables are given for the quintessence potentials for the recent average wbar_0 of the equation of state parameter, and for w_0 and w_1 in the low-z approximation w = w_0 + w_1 z. It is argued that for the exponential potential e^{lambda phi} to produce a viable present-day cosmology, lambda <= sqrt{2}. A robust, scaled numerical method is presented for simulating the cosmological evolution of the scalar field. 
Carl L. Gardner