Scalar Cosmological Perturbations
  Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a
variety of ways using Einstein's field equations, the Ricci and Bianchi
identities, or the conservation equations for the stress-energy tensor, and
possibly introducing a timelike reference congruence. The common ground is the
use of gauge invariants derived from the metric tensor, the stress-energy
tensor, or from vectors associated with a reference congruence, as basic
variables. Although there is a complication in that there is no unique choice
of gauge invariants, we will show that this can be used to advantage.
  With this in mind our first goal is to present an efficient way of
constructing dimensionless gauge invariants associated with the tensors that
are involved, and of determining their inter-relationships. Our second goal is
to give a unified treatment of the various ways of writing the governing
equations in dimensionless form using gauge-invariant variables, showing how
simplicity can be achieved by a suitable choice of variables and normalization
factors. Our third goal is to elucidate the connection between the metric-based
approach and the so-called 1+3 gauge-invariant approach to cosmological
perturbations. We restrict our considerations to linear perturbations, but our
intent is to set the stage for the extension to second order perturbations.
