# How does the equation-of-state depend on the Quintessence potential?

Quintessence fields are supposed to slowly roll down a potential V(\phi). Adding constants to the potential obviously does not change the equation of motion for this field, but it does change the pressure, energy density and equation-of-state. In particular, if I choose a sufficiently large positive consant, the equation of state
$$w = \frac{\dot \phi^2/2 - V(\phi)}{\dot \phi^2/2+V(\phi)}$$
becomes eventually indistinguishable from -1.

Shouldn't physics stay invariant in this case?

$$w = \frac{\dot \phi^2/2 - V(\phi)}{\dot \phi^2/2+V(\phi)}$$