A consistency relation for the observed galaxy bispectrum and the local non-Gaussianity from relativistic corrections

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 = 1.5, in the absence of magnification bias, we get f GR NL −3.0.

A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone

“…We use the expression up to second order for relativistic effects on the observed galaxy number counts, given in [7] (see also [8][9][10][11]). Our results hold for arbitrary triangle shapes in Fourier space, and generalize the partial result of [12], which applied a separate universe analysis to compute the relativistic effects in the special case of a squeezed bispectrum.…”

“…We also neglect the GR dynamical corrections, and we follow the standard approach of working in Fourier space, that uses the plane-parallel approximation, which affects our results on ultra-large transverse scales, k ⊥ (340 Mpc) −1 . Our key results are the nonlinear GR correction kernel (12) and the analytical form of the squeezed limit of the galaxy bispectrum (15). GR local lightcone effects in the galaxy bispectrum for isosceles shapes are shown in Figs.…”

“…In order to illustrate the nature and magnitude of the GR local lightcone corrections to the bispectrum, we choose an isosceles configuration, with k 1 = k 2 ≡ k and k 3 = k 2(1 − cos θ 12 ). We consider the cases of equilateral (θ 12 = π/3) and squeezed (θ 12 1) triangles, and we set the redshift to z = 1, for which the comoving distance from the observer to the galaxies is χ g ≈ 3.4 Gpc. For the galaxy bias, we follow [21] and take b 1 = √ 1 + z and b 2 = −0.3 √ 1 + z.…”

Detecting the relativistic galaxy bispectrum

“…Finally, further work also needs to include wide-angle effects and the effects of lensing magnification, which are excluded in the standard Fourier analysis, but have been included in a spherical Bessel analysis [36] and in the galaxy angular bispectrum [37][38][39][40].…”

Relativistic wide-angle galaxy bispectrum on the light cone

“…Recently the second-order GR effects have been derived [46][47][48][49][50][51][52][53][54][55] and include contributions such as lensing, gravitational Sachs-Wolfe (SW) and integrated Sachs-Wolfe (ISW) effects, primordial non-Gaussianity and bias (see e.g. [8,[56][57][58][59][60][61][62][63][64][65], the recent review [66] and references therein).…”