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In the present work, we generalize the theory of perturbations in adimensional space-time D + 1, where D is the number of spatial dimensions, withcosmological constant, studying scalar, vector and tensor perturbations, aswell as its structure in Newtonian and synchronous gauge. We also show thetheory of perturbations in the context of brane cosmology, where branes areembedded in a set of D-spatial dimensions, a temporal dimension, and anadditional spatial dimension. In both standard and brane cosmology, unperturbedspacetime is provided with a Friedmann-Lemaitre-Robertson-Walker metric andarbitrary sectional curvature, the matter content has the shape of a perfectfluid. In addition, we consider the arbitrary sectional curvature, obtainingthe respective equations in the Newtonian and synchronous norm. We highlightthat the results presented in this article can be used to treat brane cosmologywith a more efficient approach.

General perturbations in D+1 standard and brane cosmology revisited