Primordial non-Gaussianity in the large scale structure of the Universe

TL;DR

The paper surveys how primordial non-Gaussianity (NG) from inflation leaves detectable imprints in the large-scale structure (LSS) of the Universe, focusing on the local, equilateral, and folded bispectrum templates and their observable consequences. It details how NG propagates through linear and nonlinear density fields, influencing the mass function, halo bias, power spectra, and higher-order statistics, with particular emphasis on the scale-dependent halo bias as a smoking-gun signature of local NG. The review examines numerical simulations, halo-finding algorithms, and analytic approaches (Press-Schechter, excursion sets) to quantify NG effects on abundances and clustering, including the Ly$\alpha$ forest as an additional probe. It concludes with current constraints from LSS and prospects for future surveys, highlighting multi-tracer strategies and broadening NG shape coverage as key paths to improve sensitivity to $f_{\rm NL}^{\rm loc}$ and related parameters. The work underscores the potential of galaxy surveys to rival CMB constraints and to illuminate the physics of the early Universe, contingent on controlling systematics and modeling biases.

Abstract

Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of significant non-Gaussianity would thus have profound implications for our understanding of cosmic structure formation. The large scale mass distribution in the Universe is a sensitive probe of the nature of initial conditions. Recent theoretical progress together with rapid developments in observational techniques will enable us to critically confront predictions of inflationary scenarios and set constraints as competitive as those from the Cosmic Microwave Background. 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 (10)

• Figure 1: Skewness $\sigma\,S_3^{(1)}\!(R)$ of the smoothed density field in unit of $f_{\rm NL}^{\rm X}$ for the local, equilateral and folded bispectrum shape. The skewness for the equilateral and folded templates is a factor of $\sim 3$ smaller than in the local model. In any case, this implies that $|\sigma_R S_3(R)|\ll 1$ on the scales probed by the large scale structure for realistic values of the nonlinear coupling parameter, $|f_{\rm NL}^{\rm X}|\lesssim 100$. The shaded regions approximately indicate the range of scales probed by various LSS tracers. For the galaxy power spectrum and bispectrum, the upper limit sensitively depends upon the surveyed volume.
• Figure 2: Non-Gaussian fractional correction $\beta_\delta(k,z)= \Delta P_\delta^{\rm NG}(k,z)/P_\delta^{\rm G}(k,z)$ to the matter power spectrum that originates from primordial non-Gaussianity of the local type. Results are shown at redshift $z=0$, 0.5, 1 and 2 for $f_{\rm NL}^{\rm loc}=+100$ (filled symbols) and $f_{\rm NL}^{\rm loc}=-100$ (empty symbols). The solid curves indicate the prediction from a 1-loop perturbative expansion.
• Figure 3: Reduced matter bispectrum $Q_3$ as a function of the angle $\theta$ between ${\bf k}_1$ and ${\bf k}_2$ for a fixed $k_1=0.094\ {\rm {\it h}Mpc^{-1}}$ and $k_2=1.5 k_1$. The panels show ratios between the non-Gaussian and Gaussian $Q_3$ for $f_{\rm NL}^{\rm loc}=+100$ (top) and $-100$ (bottom). Dashed lines correspond to tree-level PT while continuous line indicate the 1-loop PT prediction.
• Figure 4: 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 various curves are theoretical prediction at $z=0$ (see text). Halos were identified using a spherical overdensity (SO) finder with a redshift-dependent overdensity threshold $\Delta_{\rm vir}(z)$ (with $\Delta_{\rm vir}(z)$ increasing from $\sim 200$ at high redshift to attain $\sim 350$ at $z=0$). Error bars denote Poisson errors. For illustration, $M=10^{15}\ {\rm M_\odot/{\it h}}$ corresponds to a significance $\nu=3.2$, 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 5: 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 in Fig. \ref{['fig:fnu1']}. The curves are the theoretical prediction Eq. (\ref{['eq:fnuthiswork']}) at $z=0$ with $q=1$ (solid) and $q=0.75$ (dotted). In the top panel, halos were identified using a spherical overdensity (SO) finder with a redshift-dependent overdensity threshold $\Delta_{\rm vir}(z)$ whereas, in the bottom panel, a Friends-of-Friends (FOF) finding algorithm with linking length $b=0.2$ was used.