  Several recent studies have shown how to properly calculate the observed
clustering of galaxies in a relativistic context, and uncovered corrections to
the Newtonian calculation that become significant on scales near the horizon.
Here, we retrace these calculations and show that, on scales approaching the
horizon, the observed galaxy power spectrum depends strongly on which gauge is
assumed to relate the intrinsic fluctuations in galaxy density to matter
perturbations through a linear bias relation. Starting from simple physical
assumptions, we derive a gauge-invariant expression relating galaxy density
perturbations to matter density perturbations on large scales, and show that it
reduces to a linear bias relation in synchronous-comoving gauge, corroborating
an assumption made in several recent papers. We evaluate the resulting observed
galaxy power spectrum, and show that it leads to corrections similar to an
effective non-Gaussian bias corresponding to a local (effective) fNL < 0.5.
This number can serve as a guideline as to which surveys need to take into
account relativistic effects. We also discuss the scale-dependent bias induced
by primordial non-Gaussianity in the relativistic context, which again is
simplest in synchronous-comoving gauge.
