A generalized local ansatz and its effect on halo bias

TL;DR

This work generalizes local primordial non-Gaussianity to include scale-dependent amplitudes via a factorizable bispectrum with two functions $\xi_s(k)$ and $\xi_m(k)$, capturing single-field and multi-field physics. Analytic predictions using peak-background split and alternative derivations show two main NG-bias signatures: a mass-dependent effective $f_{NL}^{\rm eff}(M)$ and a modified large-scale $k$-dependence $\Delta b_{NG}(k,M) \propto f_{NL}^{\rm eff}(M)\, /\, k^{2-n_f^{(m)}}$. N-body simulations reveal that halo bias indeed depends on tracer mass and scale in these generalized scenarios, with stronger signals than naive analytic expectations and a notable mass- and redshift-dependent discrepancy at low $\sigma(M)$. Forecasts for DES and LSST indicate that combining multiple mass tracers could disentangle single-field versus multi-field origins of local non-Gaussianity, though accurate modeling of halo formation remains essential for robust inference.

Abstract

Motivated by the properties of early universe scenarios that produce observationally large local non-Gaussianity, we perform N-body simulations with non-Gaussian initial conditions from a generalized local ansatz. The bispectra are schematically of the local shape, but with scale-dependent amplitude. We find that in such cases the size of the non-Gaussian correction to the bias of small and large mass objects depends on the amplitude of non-Gaussianity roughly on the scale of the object. In addition, some forms of the generalized bispectrum alter the scale dependence of the non-Gaussian term in the bias by a fractional power of k. These features may allow significant observational constraints on the particle physics origin of any observed local non-Gaussianity, distinguishing between scenarios where a single field or multiple fields contribute to the curvature fluctuations. While analytic predictions for the non-Gaussian bias agree qualitatively with the simulations, we find numerically a stronger observational signal than expected. This suggests that a more precise understanding of halo formation is needed to fully explain the consequences of primordial non-Gaussianity

Figures (5)

• Figure 1: Left panel: The effective amplitude of the non-Gaussian bias on small scales ($f_{\rm NL}^{\rm eff}$) as a function of the object's mass for two modifications of the local ansatz. The blue short dashed lines are the single field model (only $\xi_s(k)$ different from one) and the red long dashed lines are the multi-field (only $\xi_m(k)$ different from one). The upper lines show the effect of non-Gaussianity that increases on small scales, with $n_f^{(s)}=0.6$ or $n_f^{(m)}=0.3$ while the lower lines have $n_f^{(s)}=-0.6$ or $n_f^{(m)}=-0.3$. All curves are normalized to $\xi_{s,m}(k_p)=1$. Right panel: A comparison of the correction to the bias of objects of mass $4.4\times10^{14}\;h^{-1}\,M_\odot$. The solid black curve is the usual local ansatz, the blue long dashed curve is the single-field model with $n_f^{(s)}=0.6$, the red short dashed curve is the multi-field scenario with $n_f^{(m)}=0.3$, and the purple dot-dashed curve is the multi-field scenario with $n_f^{(m)}=-0.3$. Again, $\xi_{s,m}(k_p)=1$.
• Figure 2: Forecasted constraints on $f_{\rm NL}(k)$ in the model where a single field generates the curvature perturbations ( left panel) and in the multi-field model ( right panel). We show forecasts for data expected from DES (solid black curve) and LSST (dashed black curve) observations. The wavenumber at which the constraints are the best is $k_{\rm uncorr}$, and at this wavenumber the normalization and slope of the power law are precisely uncorrelated. The six colored contours on top of each panel show the individual constraints from six narrow mass bins uniformly distributed in $\log_{10}M$ from $10^{13.5}\,h^{-1}M_\odot$ to $10^{15}\,h^{-1}M_\odot$ (assuming the DES survey). In the single-field scenario, individual masses do not break degeneracy between amplitude and running of $f_{\rm NL}(k)$ and only constrain this function at a single $k$ value; combined masses are required to break the degeneracy. In the multi-field scenario, the degeneracy is broken even with halos of a fixed mass. [Note that, in all cases, the overall constraints on $f_{\rm NL}(k)$ between different wavenumbers $k$ are strongly correlated, given that we are assuming a power law in $k$.]
• Figure 3: Left panel: constraints in the $f_{\rm NL}(k_p)$-$n_f^{(s)}$ plane in the inflaton model. Lines show degeneracy directions that each of six individual mass bins suffers (these mass bins correspond to colored curves in Fig. \ref{['fig:Fisher']}). Right panel: Constraints in the $n_f^{(s)}$-$n_f^{(m)}$ plane assuming both single-field and multi-field models, and marginalizing over the amplitude (term $f_{\rm NL}(k_p)\equiv \xi_s(k_p)\xi_m(k_p)^2$ in Eq. (\ref{['eq:fnlk_forms']})).
• Figure 4: Dependence of scale-dependent non-Gaussian bias on mass, inferred from simulations. Left panel: Simulation results for the non-Gaussian contribution to the bias of halos with mass $4-8\times 10^{13}h^{-1}\,M_\odot$. The black circles points have constant $\xi_{s}(k_p)\equiv f_{NL}(k_p)=300$, the blue squares have the same $\xi_s(k_p)$ but $n_f^{(s)}=-0.6$, and the red triangles have $n_f^{(s)}=0.6$. Error bars are sample variance across several simulations with the same parameters. Right panel: The same set of curves for halos with mass $32-64\times 10^{13}h^{-1}\,M_\odot$. The scatter here is larger than in the previous plot since there are fewer objects at this mass.
• Figure 5: Simulation results for the scale-dependent non-Gaussian bias compared to theory. In the left panel, the vertical axis shows the mass-dependent ratio of the bias for non-Gaussianity that runs compared to the $f_{NL}$ constant case, measured from $f_{NL}=300$ simulations at $z=0$. The upper lines have $n_f^{(s)}=0.6$ and lower lines show $n_f^{(s)}=-0.6$. Redshifts $z=0$ (blue, higher values of $\sigma(M)$,and $z=1$ (red, lower values of $\sigma(M)$ are shown. The dashed lines are the analytical prediction, showing that agreement is better at small $\sigma(M)$. The right panel shows the same information, but plotted as a function of mass. Now the theoretical prediction (solid black lines) is redshift independent.