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.
In the upper panels, blue, orange and green lines represent the energy densities of scalar field, radiation, matter, respectively
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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.