For an exponential quintessence potential, an analytic formula links the current equation-of-state w_φ0 to the potential slope λ while enforcing prior radiation and matter domination, yielding the bound λ < 1.94 at Ω_φ0 = 0.685.
As a result, the separatrix disappears forλ > √ 6, and all trajectories that reach the present epoch originate from the ˙ϕ <0 region when solved backward in time
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Exponential Quintessence: Analytic Relationship Between the Current Equation of State Parameter and the Potential Parameter
For an exponential quintessence potential, an analytic formula links the current equation-of-state w_φ0 to the potential slope λ while enforcing prior radiation and matter domination, yielding the bound λ < 1.94 at Ω_φ0 = 0.685.