  Probes of cosmic expansion constitute the main basis for arguments to support
or refute a possible apparent acceleration due to different expansion rates in
the universe as described by inhomogeneous cosmological models. We present in
this Letter a separate argument based on results from an analysis of the growth
rate of large-scale structure in the universe as modeled by the inhomogeneous
cosmological models of Szekeres. We use the models with no assumptions of
spherical or axial symmetries. We find that while the Szekeres models can fit
very well the observed expansion history without a $\Lambda$, they fail to
produce the observed late-time suppression in the growth unless $\Lambda$ is
added to the dynamics. A simultaneous fit to the supernova and growth factor
data shows that the cold dark matter model with a cosmological constant
($\Lambda$CDM) provides consistency with the data at a confidence level of
99.65% while the Szekeres model without $\Lambda$ achieves only a 60.46% level.
When the data sets are considered separately, the Szekeres with no $\Lambda$
fits the supernova data as well as the $\Lambda$CDM does, but provides a very
poor fit to the growth data with only 31.31% consistency level compared to
99.99% for the $\Lambda$CDM. This absence of late-time growth suppression in
inhomogeneous models without a $\Lambda$ is consolidated by a physical
explanation.
