Imprint of Reionization on the Cosmic Microwave Background Bispectrum

TL;DR

This work quantifies the imprint of reionization on the CMB bispectrum by evaluating lensing-induced couplings (lensing with Doppler, ISW, and SZ effects) and Ostriker-Vishniac (OV) couplings to linear secondaries. Using Limber and non-Limber approaches within a fiducial $\Lambda$CDM cosmology and plausible reionization histories, it finds that for $\tau \lesssim 0.3$ these secondary bispectrum contributions lie below MAP's detectability and at or near Planck's sensitivity, becoming significant as noise for primordial non-Gaussianity measurements at higher $\tau$. The study also analyzes the configuration dependence and nonlinear enhancements (notably for SZ and OV), highlighting that hybrids (e.g., ISW-SZ-OV) can dominate certain OV couplings but remain largely undetectable by Planck. Overall, reionization-era secondary effects contribute small but potentially systematic bispectrum signals, emphasizing the need for precise modeling of baryonic gas, nonlinearities, and multi-frequency separation in future high-resolution CMB analyses.

Abstract

We study contributions to the cosmic microwave background (CMB) bispectrum from non-Gaussianity induced by secondary anisotropies during reionization. Large-scale structure in the reionized epoch both gravitational lenses CMB photons and produces Doppler shifts in their temperature from scattering off electrons in infall. The resulting correlation is potentially observable through the CMB bispectrum. The second-order Ostriker-Vishniac also couples to a variety of linear secondary effects to produce a bispectrum. For the currently favored flat cosmological model with a low matter content and small optical depth in the reionized epoch $τ\la 0.3$, however, these bispectrum contributions are well below the detection threshold of MAP and at or below that of Planck, given their cosmic and noise variance limitations. At the upper end of this range, they can serve as an extra source of noise for measurements with Planck of either primordial nongaussianity or that induced by the correlation of gravitational lensing with the integrated Sachs-Wolfe and the thermal Sunyaev-Zel'dovich effects. We include a discussion of the general properties of the CMB bispectrum, its configuration dependence for the various effects, and its computation in the Limber approximation and beyond.

Figures (10)

• Figure 1: Power spectrum for the temperature anisotropies in the fiducial $\Lambda$CDM model with $\tau=0.1$$(\langle z_{\rm ri} \rangle = 13\;)$$\Delta z=0.1(1+z_{\rm ri})$ (see § \ref{['sec:power']} for details). The curve labeled "primary" actually includes the small ISW, Doppler, and lensing contributions. Note that the predictions for the SZ power spectrum are highly uncertain and frequency dependent. We have also shown the instrumental noise contribution of MAP and Planck calculated using parameters in Table 1 which is important for signal-to-noise calculations.
• Figure 2: The Doppler-lensing effect. Shown are the combined Doppler and double scattering effects, ( solid line), the Doppler effect ( dotted line), and the Limber approximation to the Doppler effect ( dot-dashed line). At sufficiently high $l$, the difference between these three treatments can be ignored for most practical purposes. Top panel--- The correlation power spectrum. Bottom panel--- Contribution to $\chi^2$ per log interval in $l_3$.
• Figure 3: Dependence of the Doppler-lensing effect on the ionization optical depth for $\tau$ of 0.1, 0.3 and 0.5 with $\Delta z = 0.1(1+z_{\rm ri})$. Top panel--- The $b_l$ term for the Doppler-lensing effect. Middle panel--- CMB power spectrum used in the noise calculation. Lower panel--- The contribution to $\chi^2$ per log interval in $l_3$ with MAP and Planck detector noise included.
• Figure 4: Linear and nonlinear density power spectra for the dark matter under the Peacock & Dodds (1996) scaling approximation for our fiducial $\Lambda$CDM cosmological model evaluated at the present.
• Figure 5: Comparison of various lensing effects for our fiducial $\Lambda$CDM model and with $\tau=0.1$ and $\Delta z=0.1 (1+z_{\rm ri})$. Top panel--- The power spectrum of the correlation. Middle panel--- Contributions to $\chi^2$ per log interval in $l_3$, assuming cosmic variance only. Lower panel--- The same adding in detector noise for MAP and Planck.