Primordial non-gaussianity, statistics of collapsed objects, and the Integrated Sachs-Wolfe effect

TL;DR

This work addresses how a small local primordial non-Gaussianity characterized by $f_{NL}$ affects collapsed-object statistics and their ISW cross-correlation with the CMB. It shows that non-Gaussian initial conditions can be mapped onto Gaussian Initial conditions with a modified power spectrum, yielding analytic predictions for the halo mass function and a scale-dependent bias that enhances large-scale clustering. The authors forecast strong constraints on $f_{NL}$ from galaxy auto-correlation ($\Delta f_{NL} \sim 0.1$) and ISW-galaxy cross-correlation ($\Delta f_{NL} \sim 3$), with current cross-correlation hints suggesting $f_{NL}$ of order a few hundred. They emphasize the potential of upcoming surveys like LSST to probe early universe physics through a cosmological microscope, while acknowledging modeling limitations of the ellipsoidal collapse framework and the local non-Gaussian ansatz.

Abstract

Any hint of non-gaussianity in the cosmological initial conditions will provide us with a unique window into the physics of early universe. We show that the impact of a small local primordial non-gaussianity (generated on super-horizon scales) on the statistics of collapsed objects (such as galaxies or clusters) can be approximated by using slightly modified, but gaussian, initial conditions, which we describe through simple analytic expressions. Given that numerical simulations with gaussian initial conditions are relatively well-studied, this equivalence provides us with a simple tool to predict signatures of primordial non-gaussianity in the statistics of collapsed objects. In particular, we describe the predictions for non-gaussian mass function, and also confirm the recent discovery of a non-local bias on large scales (arXiv:0710.4560, arXiv:0801.4826) as a signature of primordial non-gaussianity. We then study the potential of galaxy surveys to constrain non-gaussianity using their auto-correlation and cross-correlation with the CMB (due to the Integrated Sachs-Wolfe effect), as a function of survey characteristics, and predict that they will eventually yield an accuracy of Delta f_{NL} ~ 0.1 and 3 respectively, which will be better than or competitive with (but independent of) the best predicted constraints from the CMB. Interestingly, the cross-correlation of CMB and NVSS galaxy survey already shows a hint of a large local primordial non-gaussianity: f_{NL} = 236 +/- 127.

Figures (8)

• Figure 1: The non-gaussian correction to $\bar{\sigma}(M)$, the effective amplitude of density fluctuations for collapsed objects of mass $M$. The solid, dotted, and dashed lines are for $z=0,1,5$ respectively, while we assumed $f_{NL}=100$. The vertical line shows $M_8$, the mass within comoving $8 h^{-1}{\rm Mpc}$.
• Figure 2: The relative change in the cluster mass function for $f_{NL} = 100$. The solid (black), dotted (red), and dashed (green) lines correspond to our analytic prediction based on the $\sigma(M)$ correction (Eq. (\ref{['dsigma8']}-\ref{['dn8']})) for $z=0,0.5$ and $1$ respectively. The triangles, squares, and pentagons are simulations of Dalal et al. Dalal:2007cu in the same order. The error bars show simple Poisson errors in simulated cluster numbers.
• Figure 3: The ratio of the elliptical to spherical collapse thresholds, as a function of the scale-independent gaussian linear bias. The scale-dependent non-gaussian bias is enhanced by this factor (Eq. \ref{['bias_ng']}).
• Figure 4: The scale-dependent part of bias $b-b_{\infty}$ divided by $b_{\infty}-1$, for $f_{NL}=100$ and $z=0$. The scale-independent part of bias, $b_{\infty} = 1.5$ and $3$ for solid and dotted curves. The dashed line is Dalal et al.'s derivation Dalal:2007cu.
• Figure 5: This figure illustrates the contrast between the gaussian and non-gaussian halo/galaxy bias. The two plots show cartoon versions of linear density vs. spatial position. The white shaded areas indicate collapse regions. For gaussian initial conditions, different Fourier modes are uncorrelated, and so long wavelength modes (thin black curve) only change the background local mean value of small scale modes (thin white curves), which in turn changes the number of density peaks that cross the collapse threshold (thick white line) and form haloes. However, for non-gaussian initial condition, the long wavelength modes can also modulate the amplitude of small scale modes, which causes an additional modulation of collapsed halo density.