Galaxy Power Spectrum in General Relativity
  We present the galaxy power spectrum in general relativity. Using a novel
approach, we derive the galaxy power spectrum taking into account all the
relativistic effects in observations. In particular, we show independently of
survey geometry that relativistic effects yield no divergent terms
(proportional to $k^{-4}P_m(k)$ or $k^{-2}P_m(k)$ on all scales) that would
mimic the signal of primordial non-Gaussianity. This cancellation of such
divergent terms is indeed expected from the equivalence principle, meaning that
any perturbation acting as a uniform gravity on the scale of the experiment
cannot be measured. We find that the unphysical infrared divergence obtained in
previous calculations occurred only due to not considering all general
relativistic contributions consistently. Despite the absence of divergent
terms, general relativistic effects represented by non-divergent terms alter
the galaxy power spectrum at large scales (smaller than the horizon scale). In
our numerical computation of the full galaxy power spectrum, we show the
deviations from the standard redshift-space power spectrum due to these
non-divergent corrections. We conclude that, as relativistic effects
significantly alter the galaxy power spectrum at $k\lesssim k_{eq}$, they need
to be taken into account in the analysis of large-scale data.
