  Increasingly accurate observations are driving theoretical cosmology toward
the use of more sophisticated descriptions of matter and the study of nonlinear
perturbations of FL cosmologies, whose governing equations are notoriously
complicated. Our goal in this paper is to formulate the governing equations for
linear perturbation theory in a particularly simple and concise form in order
to facilitate the extension to nonlinear perturbations. Our approach has
several novel features. We show that the use of so-called intrinsic gauge
invariants has two advantages. It naturally leads to: (i) a physically
motivated choice of a gauge invariant associated with the matter density, and
(ii) two distinct and complementary ways of formulating the evolution equations
for scalar perturbations, associated with the work of Bardeen and of Kodama and
Sasaki. In the first case the perturbed Einstein tensor gives rise to a second
order (in time) linear differential operator, and in the second case to a pair
of coupled first order (in time) linear differential operators. These operators
are of fundamental importance in cosmological perturbation theory, since they
provide the leading order terms in the governing equations for nonlinear
perturbations.
