Detecting the relativistic galaxy bispectrum
  The Fourier-space galaxy bispectrum is complex, with the imaginary part
arising from leading-order relativistic corrections, due to Doppler,
gravitational redshift and related line-of-sight effects in redshift space. The
detection of the imaginary part of the bispectrum is potentially a smoking gun
signal of relativistic contributions. We investigate whether next-generation
spectroscopic surveys could make such a detection. For a Stage IV spectroscopic
$H\alpha$ survey similar to Euclid, we find that the cumulative signal to noise
of this relativistic signature is $\mathcal{O}(10)$. Long-mode relativistic
effects couple to short-mode Newtonian effects in the galaxy bispectrum, but
not in the galaxy power spectrum. This is the basis for detectability of
relativistic effects in the bispectrum of a single galaxy survey, whereas the
power spectrum requires multiple galaxy surveys to detect the corresponding
signal.
