Detecting the relativistic galaxy bispectrum
Roy Maartens, Sheean Jolicoeur, Obinna Umeh, Eline M. De Weerd, Chris Clarkson, S. Camera
Abstract
The Fourier galaxy bispectrum is complex, with the imaginary part arising from \nleading-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 \npotentially a smoking gun signal of relativistic contributions. We investigate whether nextgeneration spectroscopic surveys could make such a detection. For a Stage IV spectroscopic \nHα survey similar to Euclid, we find that the cumulative signal to noise of this relativistic \nsignature is O(10). Long-mode relativistic effects couple to short-mode Newtonian effects \nin the galaxy bispectrum, but not in the galaxy power spectrum. This is the basis for \ndetectability of relativistic effects in the bispectrum of a single galaxy survey, whereas the \npower spectrum requires multiple galaxy surveys to detect the corresponding signal.