Prospects for constraining the shape of non-Gaussianity with the scale-dependent bias

TL;DR

This work investigates how the scale-dependent halo bias in large-scale structure can constrain not only the amplitude but also the shape of primordial non-Gaussianity, focusing on squeezed-limit behavior of the bispectrum. Using a quasi-single-field inflation model with a heavy isocurvaton (parameterized by $\nu$) and a model-independent power-law bias, the authors forecast how upcoming stage IV surveys could distinguish between different squeezed-limit shapes and thereby probe the inflationary dynamics. They derive the halo-bias modification $\Delta b(k,M)$ from the bispectrum via a peak-background-split framework, and perform non-Gaussian likelihood forecasts (via $\Delta\chi^2$) across redshift shells and wavenumbers. The results show that for certain fiducial models the halo bias can tighten constraints on $f_{\rm NL}$ and the squeezed-limit exponent, offering a complementary probe to CMB data and enabling discrimination among inflationary scenarios. The study also highlights the potential gains from multi-tracer analyses and cross-correlations, and discusses connections to other observational probes of squeezed-limit non-Gaussianity such as $\mu$-distortions.

Abstract

We consider whether the non-Gaussian scale-dependent halo bias can be used not only to constrain the local form of non-Gaussianity but also to distinguish among different shapes. In particular, we ask whether it can constrain the behavior of the primordial three-point function in the squeezed limit where one of the momenta is much smaller than the other two. This is potentially interesting since the observation of a three-point function with a squeezed limit that does not go like the local nor equilateral templates would be a signal of non-trivial dynamics during inflation. To this end we use the quasi-single field inflation model of Chen and Wang as a representative two-parameter model, where one parameter governs the amplitude of non-Gaussianity and the other the shape. We also perform a model-independent analysis by parametrizing the scale-dependent bias as a power-law on large scales, where the power is to be constrained from observations. We find that proposed large-scale structure surveys (with characteristics similar to the dark energy task force stage IV surveys) have the potential to distinguish among the squeezed limit behavior of different bispectrum shapes for a wide range of fiducial model parameters. Thus the halo bias can help discriminate between different models of inflation.

Figures (3)

• Figure 1: Estimated WMAP 7 constraints on $f_{\rm NL}$ at $1$--$\sigma$ coming from the overlap between the quasi-single field inflation template of Eq. \ref{['eq:template']} and the local template of Eq. \ref{['eq:local']} as defined in Eq. \ref{['eq:cosine']}.
• Figure 2: Regions in the $f_{\rm NL}$, $\nu$ parameter space defined in Eq. \ref{['eq:template']} satisfying $\Delta \chi ^2 \leq 2.3$, corresponding to the $68.3\%$ confidence level. In the squeezed limit this model behaves as $\langle \zeta^3\rangle_{q\rightarrow 0} = 1/q^{\nu + 3/2}$. We show such regions for several fiducial models, showing that the uncertainties decrease as the fiducial value of $f_{\rm NL}$ becomes larger and the fiducial value of $\nu$ approaches $1.5$, which corresponds to a bispectrum shape that behaves like the local template in the squeezed limit.
• Figure 3: Forecasts for the parametrization $\Delta b = f_{\rm NL}^p A / k^\beta$. Green regions correspond to points in the $f_{\rm NL}^p, \beta$ parameter space satisfying $\Delta \chi ^2 \leq 2.3$, corresponding to the $68.3\%$ confidence level. Note that $f_{\rm NL}^p$ is defined such that the non-Gaussian modification to the halo bias, eq. \ref{['eq:deltab']}, is the same as in the presence of a local non-Gaussianity at a scale $k = 0.03\,h\,\mathrm{Mpc}^{-1}$, thus $f_{\rm NL}(\nu=1.5)\sim 8f_{\rm NL}^p(\beta=2)$.