A Consistency Relation for the Observed Galaxy Bispectrum and the Local non-Gaussianity from Relativistic Corrections

TL;DR

This paper derives a non-perturbative consistency relation for the observed galaxy bispectrum, including relativistic effects, which helps distinguish between primordial non-Gaussianity and relativistic corrections in cosmological observations.

Contribution

It introduces a new consistency relation that accounts for relativistic effects in the galaxy bispectrum, valid at all scales and in the squeezed limit, aiding in accurate interpretation of non-Gaussian signals.

Findings

Relativistic corrections can mimic primordial non-Gaussianity with an effective f_NL of about -3.7 at redshift 1.

The consistency relation is non-perturbative and applicable at arbitrarily small scales.

Relativistic effects induce signals that could be misinterpreted as primordial non-Gaussianity.

Abstract

We obtain a consistency relation for the observed three-point correlator of galaxies. It includes relativistic effects and it is valid in the squeezed limit. Furthermore, the consistency relation is non-perturbative and can be used at arbitrarily small scales for the short modes. Our results are also useful to compute the non-linear relativistic corrections which induce a signal in the observations that might be misinterpreted as primordial non-Gaussianity with a local shape. We estimate the effective local non-Gaussianity parameter from the relativistic corrections. The exact value depends on the redshift and the magnification bias. At redshift of $ z = 1$, in the absence of magnification bias, we get $\,\, f^{\rm GR}_{\rm NL} \simeq - 3.7 $.