Approaches to linear local gauge-invariant observables in inflationary cosmologies

We review and relate two recent complementary constructions of linear local gauge-invariant observables for cosmological perturbations in generic spatially flat single-field inflationary cosmologies. After briefly discussing their physical significance, we give explicit, covariant and mutually invertible transformations between the two sets of observables, thus resolving any doubts about their equivalence. In this way, we get a geometric interpretation and show the completeness of both sets of observables, while previously each of these properties was available only for one of them.