  We use the Szekeres inhomogeneous cosmological models to study the growth of
large-scale structure in the universe including nonzero spatial curvature and a
cosmological constant. In particular, we use the Goode and Wainwright
formulation, as in this form the models can be considered to represent exact
nonlinear perturbations of an averaged background. We identify a density
contrast in both classes I and II of the models, for which we derive growth
evolution equations. By including Lambda, the time evolution of the density
contrast as well as kinematic quantities can be tracked through the matter- and
Lambda-dominated cosmic eras up to the present and into the future. In various
models of class I and class II, the growth rate is found to be stronger than
that of the LCDM cosmology, and it is suppressed at later times due to the
presence of Lambda. We find that there are Szekeres models able to provide a
growth history similar to that of LCDM while requiring less matter content and
nonzero curvature, which speaks to the importance of including the effects of
large-scale inhomogeneities in analyzing the growth of large-scale structure.
Using data for the growth factor f from redshift space distortions and the
Lyman-alpha forest, we obtain best fit parameters for class II models and
compare their ability to match observations with LCDM. We find that there is
negligible difference between best fit Szekeres models with no priors and those
for LCDM, both including and excluding Lyman-alpha data. We also find that the
growth index gamma parametrization cannot be applied in a simple way to the
growth in Szekeres models, so a direct comparison of the function f to the data
is performed. We conclude that the Szekeres models can provide an exact
framework for the analysis of large-scale growth data that includes
inhomogeneities and allows for different interpretations of observations.
(abridged)
