  Comprehensive understanding of medium-induced radiative energy loss is of a
paramount importance in describing observed jet quenching in heavy-ion
collisions. In this work, we have calculated the medium-modified gluon
splitting rates for different profiles of the expanding partonic medium, namely
profiles for static, exponential, and Bjorken expanding medium. Here in this
study, we have used the Baier-Dokshitzer-Mueller-Peigne-Schiff-Zakharov
(BDMPSZ) formalism for multiple soft scatterings with a time-dependent
transport coefficient for characterizing the expanding medium. Using the
kinetic rate equation, we have numerically evaluated the distribution of the
medium evolved gluon spectra for different medium profiles. We have presented a
calculation of the jet $Q_{AA}$ which quantifies a sensitivity of the inclusive
jet suppression on the way how the medium expands. Comparisons of predicted jet
$Q_{AA}$ with experimental data from the LHC are also presented.
