  One of the most compelling goals of observational cosmology is the
characterisation of the properties of the dark energy component thought to be
responsible for the recent acceleration of the universe, including its possible
dynamics. In this work we study phenomenological but physically motivated
classes of models in which the dark energy equation of state can undergo a
rapid transition at low redshifts, perhaps associated with the onset of the
acceleration phase itself. Through a standard statistical analysis we have used
low-redshift cosmological data, coming from Type Ia supernova and Hubble
parameter measurements, to set constraints on the steepness of these possible
transitions as well as on the present-day values of the dark energy equation of
state and in the asymptotic past in these models. We have also studied the way
in which these constraints depend on the specific parametrisation being used.
Our results confirm that such late-time transitions are strongly constrained.
If one demands a matter-like pre-transition behaviour, then the transition is
constrained to occur at high redshifts (effectively in the matter era), while
if the pre-transition equation of state is a free parameter then it is
constrained to be close to that of a cosmological constant. In any case, the
value of dark energy equation of state near the present day must also be very
similar to that of a cosmological constant. The overall conclusion is that any
significant deviations from this behaviour can only occur in the deep matter
era, so there is no evidence for a transition associated with the onset of
acceleration. Observational tools capable of probing the dynamics of the
universe in the deep matter era are therefore particularly important.
