Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase space - a review and applications

Understand

The theory of cosmological perturbations is a well elaborated field.

• To deal with the diffeomorphism invariance of general relativity one generally introduces combinations of the metric and matter perturbations which are gauge invariant up to the considered order in the perturbations.
• For linear cosmological perturbations one works with the so-called Bardeen potentials widely used in this context.
• However, there exists no common procedure to construct gauge invariant quantities also for higher order perturbations.