Model-Independent Determination of the Cosmic Growth Factor
  Since the discovery of the accelerated cosmic expansion, one of the most
important tasks in observational cosmology is to determine the nature of the
dark energy. We should build our understanding on a minimum of assumptions in
order to avoid biases from assumed cosmological models. The two most important
functions describing the evolution of the universe and its structures are the
expansion function E(a) and the linear growth factor D_+(a). The expansion
function has been determined in previous papers in a model-independent way
using distance moduli to type-Ia supernovae and assuming only a metric theory
of gravity, spatial isotropy and homogeneity. Here, we extend this analysis in
three ways: (1) We extend the data sample by combining the Pantheon
measurements of type-Ia supernovae with measurements of baryonic acoustic
oscillations; (2) we substantially simplify and generalise our method for
reconstructing the expansion function; and (3) we use the reconstructed
expansion function to determine the linear growth factor of cosmic structures,
equally independent of specific assumptions on an underlying cosmological model
other than the usual spatial symmetries. We show that the result is quite
insensitive to the initial conditions for solving the growth equation, leaving
the present-day matter-density parameter {\Omega}_m0 as the only relevant
parameter for an otherwise purely empirical and accurate determination of the
growth factor.
