Non-Gaussianity from Large-Scale Structure Surveys

TL;DR

The work surveys three complementary avenues to detect primordial non-Gaussianity in large-scale structure: higher-order correlations, the abundance of rare objects via the mass function, and the scale-dependent halo bias in clustering. It develops and contrasts two analytic frameworks for the non-Gaussian mass function (MVJ and LMSV), validates them against N-body simulations with calibration factors, and extends the analysis to voids and halo power spectra. A key result is that local-type non-Gaussianity induces a strong, scale-dependent bias on large scales, making halo clustering a powerful probe that complements CMB bispectrum constraints; the shape-dependence of the signal differs for equilateral and other templates, enabling model discrimination. The paper also discusses practical considerations for surveys (photo-z limitations, redshift-space distortions, and degeneracies with other cosmological parameters) and emphasizes the value of combining multiple observables (bispectrum, mass function, halo bias, voids) for robust detection of $f_{ m NL}$, with future data (Euclid, LSST, SZ surveys) expected to tighten constraints substantially.

Abstract

With the advent of galaxy surveys which provide large samples of galaxies or galaxy clusters over a volume comparable to the horizon size (SDSS-III, HETDEX, Euclid, JDEM, LSST, Pan-STARRS, CIP etc.) or mass-selected large cluster samples over a large fraction of the extra-galactic sky (Planck, SPT, ACT, CMBPol, B-Pol), it is timely to investigate what constraints these surveys can impose on primordial non-Gaussianity. I illustrate here three different approaches: higher-order correlations of the three dimensional galaxy distribution, abundance of rare objects (extrema of the density distribution), and the large-scale clustering of halos (peaks of the density distribution). Each of these avenues has its own advantages, but, more importantly, these approaches are highly complementary under many respects.

Figures (8)

• Figure 1: Skewness $S_{3,R}$ of the density field at $z=0$ as a function of the smoothing scale $R$ for different types of non-Gaussianity. Figure reproduced from KVJ09.
• Figure 2: Correction to the Gaussian mass function as measured in different non-Gaussian simulations. There is now agreement between different simulations. The y axis should be interpreted as $Log_{10} {\cal R}(M,z,f_{\rm NL})$. Reproduced from fig. 4 and 5 of Ref. Grossietal09.
• Figure 3: The points show the non-Gaussian correction to the mass function as measured in the N-body simulations of Grossietal09. Blue corresponds to $f_{\rm NL}=200$ and red to $f_{\rm NL}=-200$. the dashed lines correspond to the MVJ formulation and the dot-dashed lined to the LMSV formulation. In both cases the substitution $\delta_c\longrightarrow \delta_{ec}$ has been performed. The y axis should be interpreted as ${\cal R}(M,z,f_{\rm NL}=200)$. Reproduced from fig. 7 Ref. Grossietal09.
• Figure 4: The scale-dependence of the large-scale halo bias induced by a non-zero bispectrum for different types of non-Gaussianity. The dashed line corresponds to the local type and the dot-dot-dot-dashed to equilateral type. Figure reproduced from VM09.
• Figure 5: Effect of the non-Gaussian halo bias on the power spectrum. In the left-top panel we show the halo-matter cross-power spectrum for masses above $10^{13}$ M$_{\odot}$ at $z=1.02$. The left-bottom panel shows the ratio of the non-Gaussian to Gaussian bias. Figure reproduced from Grossietal09. The $f_{\rm NL}$ values reported in the figure legend should be interpreted as $f_{\rm NL}^{LSS}$. On the right panel we show the expected effect and error-bars for the large-scale power spectrum for a survey like LSST. Figure reproduced from LSSTBook.