Biasing and the search for primordial non-Gaussianity beyond the local type

TL;DR

This work develops a comprehensive framework to forecast constraints on primordial non-Gaussianity beyond the local shape using large-scale structure. It builds a general halo bias model that includes linear, non-local, non-linear, and PNG-induced terms, and computes the halo-halo power spectrum up to 1-loop within standard perturbation theory, carefully renormalizing divergent pieces. By performing MCMC forecasts with and without gradient and loop biases, the authors quantify degeneracies that degrade f_NL constraints, particularly for equilateral-type PNG, and demonstrate how multi-tracer techniques can substantially improve sensitivity, potentially beating Planck for certain beyond-local scenarios and QSFI in large-volume surveys. The paper highlights that while equilateral PNG remains challenging to constrain with power spectra alone, local PNG and QSFI hold the most promise, with multi-tracer approaches offering robust gains. Overall, the findings emphasize the complementary role of LSS, including scale-dependent bias and multi-tracer methods, alongside CMB bispectrum measurements in mapping the early-universe physics encoded in PNG.

Abstract

Primordial non-Gaussianity encodes valuable information about the physics of inflation, including the spectrum of particles and interactions. Significant improvements in our understanding of non-Gaussanity beyond Planck require information from large-scale structure. The most promising approach to utilize this information comes from the scale-dependent bias of halos. For local non-Gaussanity, the improvements available are well studied but the potential for non-Gaussianity beyond the local type, including equilateral and quasi-single field inflation, is much less well understood. In this paper, we forecast the capabilities of large-scale structure surveys to detect general non-Gaussianity through galaxy/halo power spectra. We study how non-Gaussanity can be distinguished from a general biasing model and where the information is encoded. For quasi-single field inflation, significant improvements over Planck are possible in some regions of parameter space. We also show that the multi-tracer technique can significantly improve the sensitivity for all non-Gaussianity types, providing up to an order of magnitude improvement for equilateral non-Gaussianity over the single-tracer measurement.

Figures (10)

• Figure 1: Left: Type 1) two second-order vertices. Middle: Type 2) a cubic vertex and a linear $\delta_h$. Right: Type 3) a second-order vertex and one SPT kernel $F_2$ contracted with $\delta_h$. The black dots represent the gaussian spectrum $P_{\rm G}$, and each external line carries a factor $b_{\rm full}$ (eq. \ref{['btree']}).
• Figure 2: The contributions to $P_{hh}$ compared to the linear power, $P_{\rm lin}=b_\delta^2 P_{\rm G}$. In the top panel, we show the terms linear in the extra bias coefficients, i.e. $b_{k^2} k^2 R_*^2 P_{\rm G}(k)$. For the bottom panel, we also include non-linear contributions, such as $b_{\delta^2}^2P_{\delta^2\delta^2}$. There are also terms of the form $(b_{k^2} k^2 R_*^2)^2 P_{\rm G}(k)$, but we choose not to show them here for clarity. The linear bias is chosen to be $b_\delta=3.6$, the Lagrangian radius $R_*=3.7\, {\rm Mpc}/h$, the non-Gaussianity parameter $f_{\rm NL}=1$ and all the other bias parameters are one. We show the scale-dependent bias contribution (linear in $f_{\rm NL}$ only) for $\Delta=0$ (local) and $\Delta=2$ (equilateral). At low $k$, the local ($\Delta=0$) contribution is the most important, and one can see by eye that no other bias terms can mimic its behavior. However, the $\Delta=2$ curve is both much smaller than $\Delta=0$ as well as more prone to degeneracies with non-local and non-linear contributions.
• Figure 3: Projected uncertainty on equilateral non-Gaussianity from scale-dependent bias as a function of survey volume. The solid curves show the results for our default survey assumptions and the default cutoff $k_{\rm max} \, R_* = 1/2$. The simple bias model (green) corresponds to only marginalizing over the linear bias parameter $b_\delta$. Applying a more general bias prescription leads to a severe degradation in constraining power, as seen with e.g. the purple curve (all bias terms marginalized), which is about a factor of 40 larger. The dashed green curves explore the effect of varying the small-scale cutoff while keeping the simple bias model, and the red dotted-dashed line indicates the current constraint from the CMB bispectra.
• Figure 4: Constraint on $f_{\rm NL}^{\rm Eq}$ as a function of the order at which the gradient bias expansion is truncated, relative to the constraint in the absence of gradient bias (i.e. with only the zeroth order term included). The green curves show the case without marginalizing over the loop terms in the tracer power spectrum, assuming short wavelength cutoffs $k_{\rm max} R_* = 1/4, 1/2, 1$ (circle, cross and plus markers respectively). For the default choice, $k_{\rm max} R_* = 1/2$, convergence is reached at $n_{\rm max} = 4$, which we will use as the truncation for most of this work. The orange curves show the same quantities, but including loop contributions. While the dependence on $n_{\rm max}$ is very different here, $n_{\rm max}=4$ is still a reasonable choice.
• Figure 5: The evolution of $\sigma(f_{\rm NL}^{(\Delta)})$ as a function of a fixed $\Delta$, for different marginalization schemes. The green curve is the naive scenario, where marginalizing solely over the linear bias $b_\delta$. For the orange curve, we also marginalized over gradient terms, but keeping the non-linear bias zero. The purple curve shows the full marginalization, over the every term in the expression \ref{['PhhRen']}. Up to $\Delta=1$ the behavior of the three curves is similar, and the increase with $\Delta$ comes from the fact the scales that dominate the signal get away from the squeezed limit, which is what we probe best with scale-dependent bias. At $\Delta=1$, the degeneracies start to play a more important role, as the signal is dominated by the small scales which are more non-linear and non-local. This explains the large degradation from the green to the purple curve.