Quintessence and the Transition to an Accelerating Universe

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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 zₜ = 0.5 for Omegaₗambda0 = 0.70, in agreement with the observational value zₜ = 0.46 and in mild conflict with the LambdaCDM value zₜ = 0.67. Tables are given for the quintessence potentials for the recent average wbar₀ of the equation of state parameter, and for w₀ and w₁ in the low-z approximation w = w₀ + w₁ z. It is argued that for the exponential potential elambda phi to produce a viable present-day cosmology, lambda <= sqrt2. A robust, scaled numerical method is presented for simulating the cosmological evolution of the scalar field.