The bispectrum of galaxies from high-redshift galaxy surveys: primordial non-Gaussianity and non-linear galaxy bias

TL;DR

This study forecasts how the galaxy bispectrum from high-$z$ surveys can jointly constrain linear and non-linear galaxy bias and primordial non-Gaussianity, using a Fisher-mmatrix framework that leverages all triangle configurations down to mildly non-linear scales. It analyzes local and equilateral $f_{NL}$ shapes, the impact of non-linear gravitational evolution, and redshift-space distortions, and demonstrates that high-$z$ surveys with large volumes and sufficient number density can achieve constraints competitive with or better than CMB limits. The authors also show that incorporating halo occupation distribution (HOD) priors lifts degeneracies between gravity, bias, and non-Gaussianity, significantly improving equilateral-$f_{NL}$ constraints. Collectively, the results highlight the bispectrum as a powerful probe for primordial physics and galaxy formation, with strong implications for future surveys like ADEPT and CIP.

Abstract

The greatest challenge in the interpretation of galaxy clustering data from any surveys is galaxy bias. Using a simple Fisher matrix analysis, we show that the bispectrum provides an excellent determination of linear and non-linear bias parameters of intermediate and high-z galaxies, when all measurable triangle configurations down to mildly non-linear scales, where perturbation theory is still valid, are included. The bispectrum is also a powerful probe of primordial non-Gaussianity. The planned galaxy surveys at z>2 should yield constraints on non-Gaussian parameters, f_{NL}^{loc.} and f_{NL}^{eq.}, that are comparable to, or even better than, those from CMB experiments. We study how these constraints improve with volume, redshift range, as well as the number density of galaxies. Finally, we show that a halo occupation distribution may be used to improve these constraints further by lifting degeneracies between gravity, bias, and primordial non-Gaussianity.

Figures (8)

• Figure 1: Equilateral configurations of the reduced bispectrum of dark matter distribution at the second order ("tree-level"). The horizontal lines at $Q(k)=0.57$ show the gravitational contribution only, which corresponds to $f_{NL}^{\rm loc.}=0=f_{NL}^{\rm eq.}$. The solid, long-dashed and short-dashed lines show the gravitational contribution with non-Gaussian initial perturbations at $z=0$, 1, and 4, respectively. Note that $f_{NL}^{\rm loc.}=f_{NL}^{\rm eq.}$ for equilateral configurations. ( Left panel) The curves above $Q(k)=0.57$ show $f_{NL}=+100$, while the curves below it show $f_{NL}=-100$. ( Right panel) The same as the left panel but for the current WMAP3 limits on $f_{NL}^{\rm loc.}$ (top) and $f_{NL}^{\rm eq.}$ (bottom).
• Figure 2: Configuration dependence of the reduced bispectrum of dark matter distribution from Gaussian and non-Gaussian initial conditions, as a function of an angle, $\theta$, between two wave vectors, ${\mathbf k}_1$ and ${\mathbf k}_2$, where the magnitude satisfies $k_2=2k_1=0.02~\, h \, {\rm Mpc}^{-1}$ (top panels) and $0.04~\, h \, {\rm Mpc}^{-1}$ (bottom panels). ( Left panels) $f_{NL}^{\rm loc.}=\pm 100$. ( Right panels) $f_{NL}^{\rm eq.}=\pm 200$. The dotted black line shows a Gaussian case ($f_{NL}=0$, redshift independent), while the solid, long-dashed and short-dashed lines show non-Gaussian cases at $z=0$, $1$ and $4$, respectively.
• Figure 3: ( Left panel) The halo bias functions, $b^h_1(M,z)$ (solid lines) and $b^h_2(M,z)$ (dashed lines), as a function of the mass, $M$, for $z=0$ (thick lines) and $z=1$ (thin lines) in the approximation that the formation redshift equals the observation redshift, $z=z_f$. ( Right panel) The galaxy bias parameters, $b_1$ and $b_2$, for the mean galaxy density of $n_g=5\times 10^{-3}$ (continuous lines) and $n_g=5\times 10^{-4}~h^3~{\rm Mpc}^{-3}$ (dashed lines)
• Figure 4: ( Upper panels) Predicted errors on galaxy bias parameters vs the maximum wavenumber, $k_{\rm max}$. The dashed and solid lines show the prediction for a galaxy survey at $z=1$ and 3, respectively. Each survey is assumed to have the survey volume of $V=10\, h^{-3} \, {\rm Gpc}^3$ and the number density of $n_g=5\times 10^{-3}\, h^3 \, {\rm Mpc}^{-3}$. The left panel shows the marginalized 1-$\sigma$ errors on the linear bias, $b_1$, while the right panel shows the non-linear bias, $b_2$. Both assume Gaussian initial conditions, $f_{NL}=0$. The vertical lines show $k_{\rm max}$ as determined from $\sigma(R;z) = 0.5$ for each redshift (see Sec. 3.2). ( Lower panels) Predicted errors on primordial non-Gaussian parameters vs $k_{\rm max}$. The left panel shows the marginalized 1-$\sigma$ errors on the local model, $f_{NL}^{\rm loc.}$, while the right panel shows the equilateral model, $f_{NL}^{\rm eq.}$. The bias parameters have been marginalized.
• Figure 5: Predicted 1-$\sigma$ errors on galaxy bias and primordial non-Gaussianity vs the survey volume, $V$, and redshift, $z$. The short-dashed, long-dashed and solid lines show $V=1$, $10$ and $100\, h^{-3} \, {\rm Gpc}^3$, respectively, with the galaxy number density of $n_g=5\times 10^{-3}\, h^3 \, {\rm Mpc}^{-3}$. ( Upper panels) Fractional errors on the linear bias, $b_1$ (left), and non-linear bias, $b_2$ (right), for Gaussian initial conditions, $f_{NL}=0$. ( Lower panels) Errors on primordial non-Gaussian parameters, $f_{NL}^{\rm loc.}$ (left) and $f_{NL}^{\rm eq.}$ (right), marginalized over $b_1$ and $b_2$.