Scale-Dependent Non-Gaussianity as a Generalization of the Local Model

TL;DR

This work generalizes the local model of primordial non-Gaussianity by promoting f_NL to a scale-dependent function f_NL(k) and derives the resulting bispectrum and its impact on dark matter halo bias. By formulating the bias correction within a MV/Fisher framework and adopting a piecewise-constant k-binning, the authors forecast how well future large-scale structure surveys can constrain f_NL(k) and identify the most informative scales. They introduce a principal-component decomposition of f_NL(k) to compress the data and reveal the best-measured modes, showing that the best-constrained components resemble local-type shapes while remaining distinct from equilateral-type non-Gaussianity. The paper also demonstrates how to project constraints from this basis onto other parameterizations, enabling model-specific forecasts, and proves that the generalized ansatz cannot exactly reproduce the equilateral bispectrum, clarifying the separation between these NG families. Overall, the approach provides a practical framework to connect inflationary physics to galaxy clustering and to quantify the observability of scale-dependent primordial non-Gaussianity in upcoming surveys.

Abstract

We generalize the local model of primordial non-Gaussianity by promoting the parameter fNL to a general scale-dependent function fNL(k). We calculate the resulting bispectrum and the effect on the bias of dark matter halos, and thus the extent to which fNL(k) can be measured from the large-scale structure observations. By calculating the principal components of fNL(k), we identify scales where this form of non-Gaussianity is best constrained and estimate the overlap with previously studied local and equilateral non-Gaussian models.

Figures (4)

• Figure 1: Estimated unmarginalized (left panel) and marginalized (right panel) constraints on piecewise-constant parameters $f_{\rm NL}^i$ assuming a future galaxy survey covering one-quarter of the sky out to $z = 1$, with average number density of $2\times10^{-4}$ gal/Mpc$^3$. For comparison, the green line is the constraint found for a constant $f_{\rm NL}$ using the same survey assumptions, and the red histograms are the constraints found with a lower $k_{\rm max}$ (see text for details). While the individual parameters $f_{\rm NL}^i$ are poorly constrained as expected, their few best linear combinations -- the principal components -- are well measured; see the next section and text for details.
• Figure 2: Estimated constraints obtained from future surveys with the same parameters as the previous figure at different mass smoothing scales $M_{\rm smooth}$ (labeled as $M$ in the legend). In other words, these are errors for a survey with halos of $M\gtrsim M_{\rm smooth}$.
• Figure 3: The first four principal components of $f_{\rm NL}(k)$. The PCs, $e^{(j)}(k)$, are eigenvectors of the Fisher matrix for the $f_{\rm NL}^i$, and are ordered from the best-measured one ($j=0$) to the worst-measured one ($j=19$) for the assumed fiducial survey.
• Figure 4: RMS error on each principal component, along with the cumulative error.