Gauge-Transformation Properties of Cosmological Observables and its Application to the Light-Cone Average

Understand

Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems.

• This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their theoretical description is verified by checking its gauge-invariance.
• We argue that cosmological observables are invariant scalars under diffeomorphisms and as a consequence their theoretical description is gauge-invariant, only at linear order in perturbations.
• Beyond linear order, they are usually not gauge-invariant, and we provide the general law for the gauge-transformation that the perturbation part of an observable does obey.