Cosmological Perturbations and Invariant Observables in Geodesic
  Lightcone Coordinates
  We consider a recent approach to the construction of gauge-invariant
relational observables in gravity in the context of cosmological perturbation
theory. These observables are constructed using a field-dependent coordinate
system, which we take to be geodesic lightcone coordinates. We show that the
observables are gauge-independent in the fully non-linear theory, and that they
have the expected form when one adopts the geodesic lightcone gauge for the
metric. We give explicit expressions for the Sasaki-Mukhanov variable at linear
order, and the Hubble rate -- as measured both by geodesic observers and by
observers co-moving with the inflaton -- to second order. Moreover, we show
that the well-known linearised equations of motion for the Sasaki-Mukhanov
variable and the scalar constraint variables follow from the gauge-invariant
Einstein's equations.
