Apparent Parity Violation in the Observed Galaxy Trispectrum

Recent measurements of the four-point correlation function in large-scale galaxy surveys have found apparent evidence of parity violation in the distribution of galaxies. This cannot happen via dynamical gravitational effects in general relativity. If such a violation arose from physics in the early Universe it could indicate important new physics beyond the standard model, and would be at odds with most models of inflation. It is therefore now timely to consider the galaxy trispectrum in more detail. While the four-point correlation function, or equivalently the trispectrum, its Fourier counterpart, is parity invariant, the trispectrum must take redshift-space distortions into account. Although the standard Newtonian correction also respects parity invariance, we show that subleading relativistic corrections do not. We demonstrate that these can be significant at intermediate linear scales and are dominant over the Newtonian parity-invariant part around the equality scale and above. Therefore when the galaxy four-point correlation function, we should expect to detect parity violation on large scales. Published by the American Physical Society 2024