  The potential energy from a time-dependent scalar field provides a possible
explanation for the observed cosmic acceleration. In this paper, we investigate
how data from supernova and bary acoustic oscillation surveys constrain the
possible evolution of a single scalar field over the period of time (roughly
half the age of the universe) for which these data are available. Taking a
linear approximation to the scalar potential $V(\phi) = V_0 + V_1 \phi$ around
the present value, a likelihood analysis appears to significantly prefer models
with a decreasing potential energy at present, with approximately $99.99 \%$ of
the $\exp(-\chi^2/2)$ distribution having $V_1 > 0$ in a convention where
$\dot{\phi} \le 0$ at present. The models favoured by the distribution
typically have an order one decrease $\langle |{\rm Range}[V(\phi(t))] /
V(t_0)| \rangle \approx 0.36$ in the scalar potential energy over the time
frame corresponding to $z < 2$. According to the likelihood analysis, the
$\Lambda$CDM model with no variation in dark energy appears to be significantly
disfavoured in the context of the linear potential model, but this should be
interpreted cautiously since model selection criteria that make use of $\Delta
\chi^2$ while ignoring parameter space volumes still favour $\Lambda$CDM.
Working with a second order approximation to the potential, the supernova data
can be fit well for a wide range of possible potentials, including models where
the universe has already stopped accelerating.
