  Parameters that quantify the acceleration of cosmic expansion are
conventionally determined within the standard
Friedmann-Lemaitre-Robertson-Walker (FLRW) model, which fixes spatial curvature
to be homogeneous. Generic averages of Einstein's equations in inhomogeneous
cosmology lead to models with non-rigidly evolving average spatial curvature,
and different parametrizations of apparent cosmic acceleration. The timescape
cosmology is a viable example of such a model without dark energy. Using the
largest available supernova data set, the JLA catalogue, we find that the
timescape model fits the luminosity distance-redshift data with a likelihood
that is statistically indistinguishable from the standard spatially flat
$\Lambda$ cold dark matter cosmology by Bayesian comparison. In the timescape
case cosmic acceleration is non-zero but has a marginal amplitude, with
best-fitting apparent deceleration parameter, $q_0=-0.043^{+0.004}_{-0.000}$.
Systematic issues regarding standardization of supernova light curves are
analysed. Cuts of data at the statistical homogeneity scale affect light curve
parameter fits independent of cosmology. A cosmological model dependence of
empirical changes to the mean colour parameter is also found. Irrespective of
which model ultimately fits better, we argue that as a competitive model with a
non-FLRW expansion history, the timescape model may prove a useful diagnostic
tool for disentangling selection effects and astrophysical systematics from the
underlying expansion history.
