Limits of Quintessence

We present evidence that the simplest particle-physics scalar-field models of dynamical dark energy can be separated into distinct behaviors based on the acceleration or deceleration of the field as it evolves down its potential towards a zero minimum. We show that these models occupy narrow regions in the phase plane of $w$ and $w^{\prime }$, the dark energy equation of state and its time derivative in units of the Hubble time. Restricting an energy scale of the dark energy microphysics limits how closely a scalar field can resemble a cosmological constant. These results, indicating a desired measurement resolution of order $\sigma (w^{\prime })\approx (1+w)$, define firm targets for observational tests of the physics of dark energy.