Is $w \neq -1$ evidence for a dynamical dark energy equation of state ?
  Current constraints on the dark energy equation of state parameter, $w$, are
expected to be improved by more than one order of magnitude in the next decade.
If $|w-1| \gsim 0.01$ around the present time, but the dark energy dynamics is
sufficiently slow, it is possible that future constraints will rule out a
cosmological constant while being consistent with a time-independent equation
of state parameter. In this paper, we show that although models with such
behavior can be constructed, they do require significant fine-tuning.
Therefore, if the observed acceleration of the Universe is induced by a dark
energy component, then finding $w \neq -1$ would, on its own, constitute very
strong evidence for a dynamical dark energy equation of state.
