Detecting the relativistic galaxy bispectrum

TL;DR

This paper explores the potential for next-generation galaxy surveys to detect the relativistic effects in the galaxy bispectrum, which manifest as an imaginary component due to relativistic corrections, providing a new way to test general relativity on cosmological scales.

Contribution

It demonstrates that the relativistic signature in the galaxy bispectrum can be detected with high significance in upcoming surveys, highlighting the bispectrum's unique sensitivity to relativistic effects.

Findings

Relativistic effects produce an imaginary component in the galaxy bispectrum.

Next-generation surveys can detect this relativistic signature with a signal-to-noise ratio of about 10.

The bispectrum's relativistic effects are detectable in a single survey, unlike the power spectrum.

Abstract

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.