The theory of linear cosmological perturbations is a well elaborated field and has been

successfully applied e.g. to model the structure formation in our universe. To deal with the

diffeomorphism invariance of general relativity, one usually introduces combinations of

the metric and matter perturbations which are gauge invariant under linearised diffeomorphisms.

Common choices for these linearised observables are the Bardeen potentials or the Mukhanov-Sasaki

variable.

With the relational observable formalism, in contrast, one can in principle construct observables

which are invariant up to all orders in the perturbations.

In our work we found that one can indeed re-derive the Bardeen potententials and the Mukhanov-

Sasaki variable with the observable formalism using geometrical clocks.

However, it turns out that the choice of clocks which naturally yield the Bardeen potentials at

first order leads to a non-standard observable algebra.