  We explore the effects of background cosmology on large scale structures with
non-spherical symmetry by using the concept of quasi-equilibrium which allows
certain internal properties (e.g. angular velocity) of the bodies to change
with time. In accordance with the discovery of the accelerated phase of the
universe we model the cosmological background by two representative models: the
$\Lambda$CDM Model and the Chaplygin Gas Model. We compare the effects of the
two models on various properties of large astrophysical objects. Different
equations of state are also invoked in the investigation.
