Disentangling non-Gaussianity, bias and GR effects in the galaxy distribution

TL;DR

This paper addresses disentangling local-type primordial non-Gaussianity from General Relativistic (GR) corrections and bias definitions in the galaxy distribution on large scales. It presents a GR-consistent framework for predicting observable angular power spectra $C_\ell(z)$, emphasizing that bias must be defined in the comoving-synchronous gauge and that naive Newtonian definitions can fake an $f_{ m NL}$ signal via a $k^{-2}$ bias term. The authors show that full GR corrections can produce large-scale signatures of order $f_{ m NL}=O(1)$ but with distinct redshift and scale dependence, enabling discrimination when analyzing $C_\ell(z)$. They conclude that deep, wide surveys and cross-tracer strategies are essential to overcome cosmic variance and robustly constrain primordial non-Gaussianity.

Abstract

Local non-Gaussianity, parametrized by $f_{\rm NL}$, introduces a scale-dependent bias that is strongest at large scales, precisely where General Relativistic (GR) effects also become significant. With future data, it should be possible to constrain $f_{\rm NL} = {\cal O}(1)$ with high redshift surveys. GR corrections to the power spectrum and ambiguities in the gauge used to define bias introduce effects similar to $f_{\rm NL}= {\cal O}(1)$, so it is essential to disentangle these effects. For the first time in studies of primordial non-Gaussianity, we include the consistent GR calculation of galaxy power spectra, highlighting the importance of a proper definition of bias. We present observable power spectra with and without GR corrections, showing that an incorrect definition of bias can mimic non-Gaussianity. However, these effects can be distinguished by their different redshift and scale dependence, so as to extract the true primordial non-Gaussianity.

Figures (2)

• Figure 1: Left: The power spectrum of various density perturbations at $z=1$. We use a standard LCDM background and assume $\bar{b}=2$. Right: The angular power spectrum at $z=1$ assuming all galaxies are in a Gaussian window function of width $\sigma_z=0.1$. See text for detailed explanation. Note that we take $f_{\rm NL}=0.63$, which is slightly different from $f_{\rm NL}=3/A$ due to the effect of the cosmological constant. Also $A$ evolves with redshift and a different $f_{\rm NL}$ would be required at another redshift.
• Figure 2: Ratio of the standard angular power spectra to the full GR spectrum in various cases. See text for detailed explanation. We assume $\bar{b}=2$ and all the galaxies are in a Gaussian window function of width $\sigma_z=0.1 z$.