The observed galaxy power spectrum in General Relativity
  Measurements of the clustering of galaxies in Fourier space, and at low
wavenumbers, offer a window into the early Universe via the possible presence
of scale dependent bias generated by Primordial Non Gaussianites. On such large
scales a Newtonian treatment of density perturbations might not be sufficient
to describe the measurements, and a fully relativistic calculation should be
employed. The interpretation of the data is thus further complicated by the
fact that relativistic effects break statistical homogeneity and isotropy and
are potentially divergent in the Infra-Red (IR). In this work we compute for
the first time the ensemble average of the most used Fourier space estimator in
spectroscopic surveys, including all general relativistic (GR) effects, and
allowing for an arbitrary choice of angular and radial selection functions. We
show that any observable is free of IR sensitivity once all the GR terms,
individually divergent, are taken into account, and that this cancellation is a
consequence of the presence of the Weinberg adiabatic mode as a solution to
Einstein's equations. We then study the importance of GR effects, including
lensing magnification, in the interpretation of the galaxy power spectrum
multipoles, finding that they are in general a small, less than ten percent
level, correction to the leading redshift space distortions term. This work
represents the baseline for future investigations of the interplay between
Primordial Non Gaussianities and GR effects on large scales and in Fourier
space.
