  In this work the collapsing process of a spherically symmetric star, made of
dust cloud, in the background of dark energy is studied for two different
gravity theories separately, i.e., DGP Brane gravity and Loop Quantum gravity.
Two types of dark energy fluids, namely, Modified Chaplygin gas and Generalised
Cosmic Chaplygin gas are considered for each model. Graphs are drawn to
characterize the nature and the probable outcome of gravitational collapse. A
comparative study is done between the collapsing process in the two different
gravity theories. It is found that in case of dark matter, there is a great
possibility of collapse and consequent formation of Black hole. In case of dark
energy possibility of collapse is far lesser compared to the other cases, due
to the large negative pressure of dark energy component. There is an increase
in mass of the cloud in case of dark matter collapse due to matter
accumulation. The mass decreases considerably in case of dark energy due to
dark energy accretion on the cloud. In case of collapse with a combination of
dark energy and dark matter, it is found that in the absence of interaction
there is a far better possibility of formation of black hole in DGP brane model
compared to Loop quantum cosmology model.
