Non-Gaussianity and the CMB Bispectrum: confusion between Primordial and Lensing-Rees Sciama contribution?

TL;DR

This work assesses whether the CMB bispectrum from the primary-lensing-Rees-Sciama (L-RS) cross-correlation can masquerade as local-type primordial non-Gaussianity parametrized by $f_{NL}$. By formulating both the primary and L-RS bispectra and computing their expected signal-to-noise using Halofit and Peacock & Dodds non-linear clustering, the authors show that L-RS can induce an effective $f_{NL}$ of about 10 for typical high-$\ell$ analyses, particularly in squeezed configurations. They analyze the shape dependence and find that, while some squeezed configurations exhibit near-degeneracy with the local signal, overall the two bispectra imprint different features that could be disentangled with careful modeling; nonetheless, ignoring L-RS leads to biases that exceed future experimental uncertainties. The study concludes that forthcoming CMB measurements must include L-RS contributions in bispectrum analyses, and emphasizes the need for accurate non-linear modeling, ideally via simulations, to obtain robust constraints on primordial non-Gaussianity.

Abstract

We revisit the predictions for the expected Cosmic Microwave Background bispectrum signal from the primary-lensing-Rees-Sciama correlation; we point out that it can be a significant contaminant to the bispectrum signal from primordial non-Gaussianity of the local type. This non-Gaussianity, usually parameterized by the non-Gaussian parameter f_NL, arises, for example, in multi-field inflation. In particular both signals are frequency independent, and are maximized for nearly squeezed configurations. While their detailed scale-dependence and harmonic imprints are different for generic bispectrum shapes, we show that, if not included in the modeling, the primary-lensing-Rees-Sciama contribution yields an effective f_{NL} of 10 when using a bispectrum estimator optimized for local non-Gaussianity. Considering that expected 1-sigma errors on f_{NL} are < 10 from forthcoming experiments, we conclude that the contribution from this signal must be included in future constraints on f_{NL} from the Cosmic Microwave Background bispectrum.

Figures (4)

• Figure 1: TOP-LEFT panel: The non-linear matter power spectrum $P_\delta^{NL}(k)$ obtained with Halofit (solid line) and by using the Peacock & Dodds (PD) semi-analytical approach (dot-dashed line). The upper curves refer to redshift $z=0.1$, while the lower curves to $z=1$. BOTTOM-LEFT panel: The absolute value of the $\cal Q (\ell)$ L-RS bispectrum coefficients defined in Eq.(\ref{['ql']}), plotted as a function of the angular scale $\ell$. The cusp indicates where ${\cal Q}$ changes sign due to the onset of non-linearities; in linear theory $\cal Q$ is always positive (dashed line). The solid line corresponds to the coefficients obtained by using the Halofit non-linear matter power spectra $P^{NL}_{\Phi}(k,z)$, while the dot-dashed line refers to the $\cal Q (\ell)$ obtained with the PD semi-analytical method to model the non-linear behavior. The cosmological parameters used are listed in Tab. \ref{['t:param']}. Note that the non-linear transition in the two cases happens at different scales: the $\cal Q (\ell)$ from Halofit change sign at $\ell \simeq 210$, while the ones from the PD at $\ell \simeq 300$. BOTTOM-RIGHT panel: Signal-to-noise ratio --Eq. (\ref{['sn']})-- for the secondary Lensing-Rees Sciama Bispectrum as a function of $\ell_{max}$ in the case of an all sky, cosmic variance limited experiment (solid line). The dashed line refers to the signal-to-noise for the Lensing- linear Integrated Sachs Wolfe bispectrum. TOP-RIGHT panel: The dot-dashed line is the $\chi^2$ between the L-RS bispectra obtained respectively with Halofit and with PD, as defined in Eq. \ref{['chiPD']}. The dashed line represents the same quantity, but now the comparison is between the L-RS (Halofit) and the Lensing- linear ISW bispectra. Both quantities are plotted as a function of the maximum multipole $\ell_{max}$.
• Figure 2: Effective non-linear parameter $f_{NL}^{L-RS}$ (Eq. \ref{['fnl-l-rs']}, left panels) and corresponding reduced L-RS (solid) and Primary (Dashed) bispectra (right panels) for two nearly squeezed configurations: $\ell_1=2, \, \ell_2 > 40, \, \ell_3=\ell_2+2$ (top panels) and $\ell_1=2, \, \ell_2 > 40, \, \ell_3=\ell_2$ (bottom panels). In the right panels the primary bispectrum plotted has $f_{NL}=-10$ for making it more visible. Note that in the case illustrated in the bottom panels, the two bispectra have exactly the same shape and they are completely degenerate for a $f_{NL} \simeq -17$.
• Figure 3: Reduced bispectra $b_{l_1l_2l_3}$: Primary for $f_{nl}=-10$ (dashed line) and Lensing-Rees Sciama (solid line). The left plot shows equilateral triangle configurations $\ell=\ell_1=\ell_2=\ell_3$, while the right one shows the flattened configurations $\ell_1=2 \ell_3$ and $\ell_2=\ell_3$. We have plotted $b^{L-RS}_{l_1l_2l_3} \ell_1^2 (\ell_1+1)^2 \,10^{16}$, which makes the Sachs-Wolfe plateau of the Primary reduced bispectrum easily seen at large angular scales.
• Figure 4: The plot shows $\hat{f}_{NL}$, as defined in Eq. \ref{['eq:fnl-est']}, as a function of $\ell_{max}$. The dashed line refers to $\hat{f}_{NL}$ obtained by summing over all configurations, while the dot-dashed line refers to $\hat{f}_{NL}$ obtained from nearly squeezed configuration (where $\ell_1$ runs from 2 to 10, $\ell_2$ from 50$\ell_1$ to $\ell_{max}$ and $\ell_3$ from $\ell_2$ to $\ell_{max}$), which dominate for both the primary (local type) and the lensing-Rees Sciama bispectrum. The solid lines indicates where the bias is negative.