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 ΛCDM model at low redshifts 0 ≤ z ≤ 5. However, for a natural range of initial values of the quintessence field, the SUGRA and Polónyi potentials predict a transition redshift z_t ≈ 0.5 for Ω_Λ0, in agreement with the observational value z_t ≈ 0.46 and in mild conflict with the ΛCDM value z_t = 0.67. Tables are given for the quintessence potentials for the recent average ̄w₀ of the equation of state parameter, and for w₀ and w₁ in the low-z approximation w ≈ w₀ + w₁z. It is argued that for the exponential potential e^λφ to produce a viable present-day cosmology, λ ≤ 2. A robust, scaled numerical method is presented for simulating the cosmological evolution of the scalar field.