Constraints on local primordial non-Gaussianity from large scale structure

TL;DR

This work assesses how local primordial non-Gaussianity, parameterized by $f_{ m NL}$, imprints a scale-dependent bias on large-scale structure. It derives a general, merger-aware framework for the non-Gaussian bias using peak-background split and extended Press-Schechter theory, and then constrains $f_{ m NL}$ by combining SDSS-based tracers (LRGs, QSOs) and ISW cross-correlations with CMB data. The results show no evidence for nonzero $f_{ m NL}$, with competitive constraints to WMAP5 bispectrum; allowing quasar assembly histories to affect bias weakens the limits but remains informative. The study underscores the promise and limitations of large-scale structure as a probe of primordial non-Gaussianity and calls for simulations and deeper surveys to sharpen the method.

Abstract

Recent work has shown that the local non-Gaussianity parameter f_NL induces a scale-dependent bias, whose amplitude is growing with scale. Here we first rederive this result within the context of peak-background split formalism and show that it only depends on the assumption of universality of mass function, assuming halo bias only depends on mass. We then use extended Press-Schechter formalism to argue that this assumption may be violated and the scale dependent bias will depend on other properties, such as merging history of halos. In particular, in the limit of recent mergers we find the effect is suppressed. Next we use these predictions in conjunction with a compendium of large scale data to put a limit on the value of f_NL. When combining all data assuming that halo occupation depends only on halo mass, we get a limit of -29 ~ (-65)< f_NL < +70 ~(+93) at 95% (99.7%) confidence. While we use a wide range of datasets, our combined result is dominated by the signal from the SDSS photometric quasar sample. If the latter are modeled as recent mergers then the limits weaken to -31 ~(-96) < f_NL < +70 ~ (+96) . These limits are comparable to the strongest current limits from the WMAP 5 year analysis, with no evidence of a positive signal in f_NL. While the method needs to be thoroughly tested against large scale structure simulations with realistic quasar and galaxy formation models, our results indicate that this is a competitive method relative to CMB and should be further pursued both observationally and theoretically.

Figures (5)

• Figure 1: The correlation of each quasar sample with stars and with the red stars.
• Figure 2: The window functions for the $\ell=6$ and $\ell=18$ bins of the quasar power spectrum.
• Figure 3: This figure shows 6 datasets that are most relevant for our constraints on the value of $f_{\rm NL}$. In the left column show the NVSSxCMB Integrate Sach Wolfe Cross correlation, the QSO1 power spectrum, the spectroscopic LRG power spectrum, while the right column shows the last three slices of the photometric LRG sample. The lines show the best fit $f_{\rm NL}=0$ model (black, solid) and two non-Gaussian models: $f_{\rm NL}=100$ (blue, dotted), $f_{\rm NL}=-100$ (red, dashed). The ISW panel additionally shows the $f_{\rm NL}=800$ model as green, dot-dashed line. While changing $f_{\rm NL}$, other cosmological parameters were kept fixed. See text for further discussion.
• Figure 4: This figure shows the median value (red points) and 1,2 and 3-sigma limits on $f_{\rm NL}$ obtained from different probes (vertical lines). The data set used are, from top to bottom: Photometric LRGs, Photometric LRGs with only slices 0--4 used, Spectroscopic LRGs, Integrated Sach Wolfe effect, photometric QSO, photometric QSOs using $b(z) \propto 1/D(z)$ biasing scheme (see Section \ref{['sec:phot-quas-from']}), photometric QSOs using alternative $\chi^2$ calculation scheme (see Section \ref{['sec:phot-quas-from']}), using a scale dependent bias formula appropriate for recently merged halos (Section \ref{['sec:halo-merger-bias']}), Combined sample, Combined sample using a scale dependent bias formula appropriate for recently merged halos (for QSO), the last two resoluts to which a statistically independent WMAP 5 bispectrum $f_{\rm NL}$ constraint was added. See text for discussion.
• Figure 5: This figure shows 1 and 2$\sigma$ contours on the $n_s$-$f_{\rm NL}$ plane for our best combined data set with additional WMAP 5 year bispectrum constraint (assumed to be independent of $n_s$). Red lines are predictions from the ekpyrotic models and correspond to values of fixed $\gamma$ and varying $\epsilon$. Different line correspond to different values of $\gamma$, which varies between $\gamma=-1$ (flat, constant, negative $f_{\rm NL}$) to $\gamma=-0.2$ in steps of $0.1$. The dashed green line corresponds to the theoretically favored value of $\gamma=-1/\sqrt{3}$ according to 2008PhRvD..77b3516L.