Local stochastic non-Gaussianity and N-body simulations

TL;DR

This study tests predictions for local-type primordial non-Gaussianity in a two-field curvaton-inflaton model using N-body simulations. It confirms that a nonzero inflaton-curvaton ratio $\xi$ induces large-scale stochastic halo bias, but the amplitude is overpredicted by about 30% relative to peak-background split expectations; halo bias remains broadly consistent with PB-split predictions within ~10%. The Gaussian case reveals significant mismatches between halo-model stochasticity and simulations, highlighting the difficulty of semi-analytic stochasticity modeling. Overall, the results validate the qualitative utility of PB-split for connecting early-universe physics to large-scale structure while underscoring the need for simulations to obtain precise, data-relevant predictions for $f_{NL}$ and $\xi$.

Abstract

Large-scale clustering of highly biased tracers of large-scale structure has emerged as one of the best observational probes of primordial non-Gaussianity of the local type (i.e. f_{NL}^{local}). This type of non-Gaussianity can be generated in multifield models of inflation such as the curvaton model. Recently, Tseliakhovich, Hirata, and Slosar showed that the clustering statistics depend qualitatively on the ratio of inflaton to curvaton power ξafter reheating, a free parameter of the model. If ξis significantly different from zero, so that the inflaton makes a non-negligible contribution to the primordial adiabatic curvature, then the peak-background split ansatz predicts that the halo bias will be stochastic on large scales. In this paper, we test this prediction in N-body simulations. We find that large-scale stochasticity is generated, in qualitative agreement with the prediction, but that the level of stochasticity is overpredicted by ~30%. Other predictions, such as ξindependence of the halo bias, are confirmed by the simulations. Surprisingly, even in the Gaussian case we do not find that halo model predictions for stochasticity agree consistently with simulations, suggesting that semi-analytic modeling of stochasticity is generally more difficult than modeling halo bias.

Figures (4)

• Figure 1: Halo bias $b_{mi}(k)$ for selected redshifts and halo mass bins, estimated from $N$-body simulations as described in Appendix \ref{['app:estimators']}. The curves are the predicted form in Eq. (\ref{['eq:bias_prediction']}), with $b_0$ treated as a free parameter which is fit from data.
• Figure 2: Diagonal components $r_{ii}$ of the stochasticity statistic defined in Eq. (\ref{['eq:rijdef']}), estimated from $N$-body simulations as described in Appendix \ref{['app:estimators']}, for varying choices of redshift, halo mass range, and curvaton model parameters ($f_{NL}$, $\xi$).
• Figure 3: Stochasticity parameter $r_{ii}$ estimated from Gaussian simulations (error bars), with halo model prediction shown for comparison (curves). In general, we do not find that the halo model accurately predicts $r_{ii}$. An example of a redshift and mass bin where the halo prediction disagrees with simulation ($z=2$ and $M > 1.15 \times 10^{13}$$h^{-1}M_\odot$) and an example where the two agree ($z=0.5$ and $M > 4.66 \times 10^{13}$$h^{-1}M_\odot$) are shown.
• Figure 4: Change in stochasticity parameter $\Delta r_{ii} = r_{ii}(k,f_{NL},\xi) - r_{ii}(k,f_{NL}=0)$ between the curvaton model with $(f_{NL},\xi)=(500,1)$ and the Gaussian case, estimated from $N$-body simulations. The peak-background split (solid curve) overpredicts the level of stochasticity, but excellent agreement with simulation is obtained by scaling the prediction by $q=0.42$ (dotted). When the parameters ($f_{NL}$,$\xi$,$z$) and the halo mass range are varied, we find that scaling the peak-background split prediction always provides a good fit, but the value of $q$ varies, as shown in Tab. \ref{['tab:q']}.