Primordial non-Gaussianity from the large scale structure

TL;DR

Primordial non-Gaussianity (NG) offers a window into inflationary physics beyond Gaussian perturbations. The paper surveys how NG shapes (local, equilateral, folded) propagate into large-scale structure via mass function, halo bias, voids, galaxy clustering, bispectrum, and Lyα forest, using analytic approaches and N-body simulations. It highlights the dominant role of the scale-dependent halo bias in local NG as a key LSS observable, discusses the impact of halo finding and observational systematics, and reviews current constraints and future prospects, including multi-tracer strategies to beat cosmic variance. The work emphasizes that upcoming all-sky surveys could achieve constraints competitive with, or surpassing, CMB limits, especially with improved mass calibration and analysis of multiple NG shapes.

Abstract

Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of non-Gaussianity would have profound implications for our understanding of cosmic structure formation. In this paper, we review past and current efforts in the search for primordial non-Gaussianity in the large scale structure of the Universe.

Figures (4)

• Figure 1: Fractional deviation from the Gaussian mass function as a function of the peak height $\nu=\delta_{\rm c}/\sigma$. Different symbols refer to different redshifts as indicated. The solid curve is the theoretical prediction Eq. (\ref{['eq:fnuthiswork']}) at $z=0$ based on an Edgeworth expansion of the dark matter probability distribution function. In the top panel, halos are identified using a spherical overdensity (SO) finder with a redshift-dependent overdensity threshold $\Delta_{\rm vir}(z)$. In the middle panel, a Friends-of-Friends (FOF) finding algorithm with linking length $b=0.2$ is used. The bottom panel shows the effect of decreasing the FOF mass by 20% (see text). In all panels, error bars denote Poisson errors. For illustration, $M=10^{15}\ {\rm M_\odot/{\it h}}$ corresponds to $\nu=3.2$, 5.2, 7.7 at redshift $z=0$, 1 and 2, respectively. Similarly, $M=10^{14}\ {\rm M_\odot/{\it h}}$ and $10^{13}\ {\rm M_\odot/{\it h}}$ correspond to $\nu=1.9$, 3, 4.5 and 1.2, 1.9, 2.9 respectively.
• Figure 2: Halo-halo and halo-matter power spectra $P_{\rm h}(k)$ and $P_{{\rm h}\delta}(k)$ measured in simulations of the Gaussian model and of the local $f_{\rm NL}^{\rm loc}$ type with $f_{\rm NL}^{\rm loc}=\pm 100$. Halos of mass $M>2\times 10^{13}\ {\rm M_\odot/{\it h}}$ were identified at redshift $z=2$ with a SO finder. The linear Gaussian bias of this sample is $b_1(M)=2.53$. The error bars represent the scatter among 8 realizations. The solid and dashed curve show the theoretical $P_{\rm h}(k)$ and $P_{{\rm h}\delta}(k)$ obtained wih the non-Gaussian bias correction Eq.(\ref{['eq:dbias']}). For $f_{\rm NL}^{\rm loc}=-100$, the cross-power spectrum is negative on scales $k\lesssim 0.005\ {\rm {\it h}Mpc^{-1}}$, in good agreement with the theoretical prediction.
• Figure 3: Fractional correction to the Gaussian halo bias in the $f_{\rm NL}^{\rm loc}=\pm 100$ and Gaussian models. In constrast to Fig. \ref{['fig:powng']}, halos were identified with a FOF finder of linking length $b=0.2$. Only the wavemodes to the left of the vertical line were used to fit $\Delta b_\kappa(k,f_{\rm NL}^{\rm loc})$. The best-fit value of $f_{\rm NL}^{\rm loc}$ and the corresponding 1$\sigma$ error is quoted for each model (Figure taken from nicohamaus).
• Figure 4: Ratio between the Lyman-$\alpha$ 3D flux power spectrum extracted from simulations of Gaussian and non-Gaussian initial conditions at redshift $z=2$. The mean transmission is set to $\bar{F}=0.8$ (Figure taken from shirleyho).