From matter to galaxies: General relativistic bias for the one-loop
  bispectrum
  We write down the Lagrangian bias expansion in general relativity up to 4th
order in terms of operators describing the curvature of an early-time
hypersurface for comoving observers. They can be easily expanded in synchronous
or comoving gauges. This is necessary for the computation of the one-loop halo
bispectrum, where relativistic effects can be degenerate with a primordial
non-Gaussian signal. Since the bispectrum couples scales, an accurate
prediction of the squeezed limit behavior needs to be both non-linear and
relativistic. We then evolve the Lagrangian bias operators in time in comoving
gauge, obtaining non-local operators analogous to what is known in the
Newtonian limit. Finally, we show how to renormalize the bias expansion at an
arbitrary time and find that this is crucial in order to cancel unphysical
$1/k^2$ divergences in the large-scale power spectrum and bispectrum that could
be mistaken for a contamination to the non-Gaussian signal.
