What can be learned about dark energy evolution?

We examine constraints obtained from SNIa surveys on a two parameter model of dark energy in which the equation of state $w (z) = P(z) / \rho (z)$ undergoes a transition over a period significantly shorter than the Hubble time. We find that a transition between $w \sim -0.2$ and $w \sim -1$ (the first value being somewhat arbitrary) is allowed at redshifts as low as 0.1, despite the fact that data extend beyond $z \sim 1$. Surveys with the precision anticipated for space experiments should allow only slight improvement on this constraint, as a transition occurring at a redshift as low as ~0.17 could still remain undistinguishable from a standard cosmological constant. The addition of a prior on the matter density $\Omega_{\rm m}= 0.3$ only modestly improves the constraints. Even deep space experiments would still fail to identify a rapid transition at a redshift above 0.5. These results illustrate that a Hubble diagram of distant SNIa alone will not reveal the actual nature of dark energy at a redshift above 0.2 and that only the local dynamics of the quintessence field can be inferred from a SNIa Hubble diagram. Combinations, however, seem to be very efficient: we found that the combination of present day CMB data and SNIa already excludes a transition at redshifts below 0.8