The Odd-Parity Part of the Observed Galaxy Trispectrum

TL;DR

This paper investigates the relativistic effects on the galaxy trispectrum in redshift space, focusing on parity violation signals that could reveal new physics from inflation, while accounting for observational biases.

Contribution

It calculates the leading-order relativistic corrections to the galaxy trispectrum and analyzes their impact on detecting parity violation in large-scale structure surveys.

Findings

Relativistic effects induce a parity-odd component in the galaxy trispectrum.

Parameter choices significantly influence the magnitude of relativistic corrections.

Different survey configurations affect the detectability of parity-violating signals.

Abstract

Recently the galaxy matter density 4-point correlation function has been looked at to investigate parity violation in large scale structure surveys. The 4-point correlation function is the lowest order statistic which is sensitive to parity violation, since a tetrahedron is the simplest shape that cannot be superimposed on its mirror image by a rotation. If the parity violation is intrinsic in nature, this could give us a window into inflationary physics. However, we need to exhaust all other contaminations before we consider them to be intrinsic. Even though the standard Newtonian redshift-space distortions are parity symmetric, the full relativistic picture is not. Therefore, we expect a parity-odd trispectrum when observing in redshift space. We calculate the trispectrum with the leading-order relativistic effects and investigate in detail the parameter space of the trispectrum and the effects of these relativistic corrections for different parameter values and configurations. We also look at different surveys and how the evolution and magnification biases can be affected by different parameter choices.