  We discuss the evolution equations for the linear scalar perturbations for
two reference field models: the Brown-Kucha\v{r} and Gaussian dust models, both
of which involve three scalar physical degrees of freedom. We introduce a set
of gauge invariant variables on the reduced phase space of the dust models that
is suitable for comparing our results with those of the conventional approach.
Due to the additional two physical degrees of freedom, the Bardeen and
Mukhanov-Sasaki equations involve additional dust contributions and are part of
a system of three coupled differential equations that describes the evolution
of the scalar perturbations. Our choice of gauge invariant variables takes into
account the two-fluid description of the dust models for the spatially flat
Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime as the background. Our
analysis extends earlier results for the two dust models in the relational
formalism by making them directly comparable to conventional techniques and
facilitate a numerical analysis of the evolution equations. Similar to previous
results on geometrical clocks our analysis shows that even for two-fluid
systems, there is a natural choice of the set of gauge invariant variables for
each chosen gauge which not only offers a direct physical interpretation but
also results in simplifications to the dynamical equations.
