  With the help of families of density contrast indicators, we study the
tendency of gravitational systems to become increasingly lumpy with time.
Depending upon their domain of definition, these indicators could be local or
global. We make a comparative study of these indicators in the context of
inhomogeneous cosmological models of Lemaitre--Tolman and Szekeres. In
particular, we look at the temporal asymptotic behaviour of these indicators
and ask under what conditions, and for which class of models, they evolve
monotonically in time. We find that for the case of ever-expanding models,
there is a larger class of indicators that grow monotonically with time,
whereas the corresponding class for the recollapsing models is more restricted.
Nevertheless, in the absence of decaying modes, indicators exist which grow
monotonically with time for both ever-expanding and recollapsing models
simultaneously. On the other hand, no such indicators may found which grow
monotonically if the decaying modes are allowed to exist. We also find the
conditions for these indicators to be non-divergent at the initial singularity
in both models. Our results can be of potential relevance for understanding
structure formation in inhomogeneous settings and in debates regarding
gravitational entropy and arrow of time. In particular, the spatial dependence
of turning points in inhomogeneous cosmologies may result in multiple density
contrast arrows in recollapsing models over certain epochs. We also find that
different notions of asymptotic homogenisation may be deduced, depending upon
the density contrast indicators used.
