  In the present work, we generalize the theory of perturbations in a D + 1
dimensional space-time with cosmological constant, studying scalar, vector and
tensor perturbations, as well as its structure in Newtonian and Synchronous
gauge. We also show the theory of perturbations in the context of brane
cosmology, where branes are embedded in a set of D-spatial dimensions, a
temporal dimension, and an additional spatial dimension. In both, standard and
brane cosmology an unperturbed spacetime is provided with a
Friedmann-Lemaitre-Robertson-Walker metric and arbitrary sectional curvature,
the matter content has the shape of a perfect fluid. In addition, we consider
the arbitrary sectional curvature, obtaining the respective equations in the
Newtonian and Synchronous gauge. We highlight that the results presented in
this article can be used to treat brane cosmology with two concentric branes or
tackle the \sigma_{8} tension with a braneworld approach. Finally, as an
example of the utility of all the technology presented in this paper, we show
an application to the energy ux and the repercussions in the framework of the
brane-worlds.
