  We present a field-based approach to the analysis of cosmic shear data to
infer jointly cosmological parameters and the dark matter distribution. This
forward modelling approach samples the cosmological parameters and the initial
matter fluctuations, using a physical gravity model to link the primordial
fluctuations to the non-linear matter distribution. Cosmological parameters are
sampled and updated consistently through the forward model, varying (1) the
initial matter power spectrum, (2) the geometry through the distance-redshift
relationship, and (3) the growth of structure and light-cone effects. Our
approach extracts more information from the data than methods based on
two-point statistics. We find that this field-based approach lifts the strong
degeneracy between the cosmological matter density, $\Omega_\mathrm{m}$, and
the fluctuation amplitude, $\sigma_8$, providing tight constraints on these
parameters from weak lensing data alone. In the simulated four-bin tomographic
experiment we consider, the field-based likelihood yields marginal
uncertainties on $\sigma_8$ and $\Omega_\mathrm{m}$ that are, respectively, a
factor of 3 and 5 smaller than those from a two-point power spectrum analysis
applied to the same underlying data.
