Observed galaxy number counts on the lightcone up to second order: II. Derivation

Understand

We present a detailed derivation of the observed galaxy number over-density on cosmological scales up to second order in perturbation theory.

• We include all relativistic effects that arise from observing on the past lightcone.
• The derivation is in a general gauge, and applies to all dark energy models (including interacting dark energy) and many modified gravity models.
• The result will be important for accurate cosmological parameter estimation, including non-Gaussianity, since all projection effects need to be taken into account.