Large-Scale Structure Observables in General Relativity
  We review recent studies that rigorously define several key observables of
the large-scale structure of the Universe in a general relativistic context.
Specifically, we consider i) redshift perturbation of cosmic clock events; ii)
distortion of cosmic rulers, including weak lensing shear and magnification;
iii) observed number density of tracers of the large-scale structure. We
provide covariant and gauge-invariant expressions of these observables. Our
expressions are given for a linearly perturbed flat Friedmann-Robertson-Walker
metric including scalar, vector, and tensor metric perturbations. While we
restrict ourselves to linear order in perturbation theory, the approach can be
straightforwardly generalized to higher order.
