Detecting the relativistic galaxy bispectrum
Abstract
The Fourier galaxy bispectrum is complex, with the imaginary part arising from
leading-order relativistic corrections, due to Doppler, gravitational redshift and related lineof-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 nextgeneration spectroscopic surveys could make such a detection. For a Stage IV spectroscopic
Hα survey similar to Euclid, we find that the cumulative signal to noise of this relativistic
signature is 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.