Crinkles in the last scattering surface: Non-Gaussianity from inhomogeneous recombination

TL;DR

This work analyzes a second-order CMB bispectrum sourced by perturbations in the electron density during recombination, $ _e$, which can be several times larger than baryon perturbations. Using DRECFAST and line-of-sight integration, the authors derive $ heta^{(2)}_{\ell m}$ from $ _e$-driven terms and compute the angular-averaged bispectrum $B^{\ell_1\\ell_2\ell_3}$, comparing it to the local-type primordial bispectrum characterized by $f_{ m NL}$. The recombination bispectrum peaks in squeezed configurations and, for high $ ext{l}_{max}$, has an amplitude comparable to $f_{ m NL}$-type primordial signals with an effective $f_{ m NL}$ in the range $oxed{0.05 ext{ to } -1}$ depending on the $( ext{l}_1, ext{l}_2, ext{l}_3)$ configuration, though it remains below Planck’s detectability. The study highlights a qualitative similarity in shape to local-type non-Gaussianity, underscoring the need for a full second-order Boltzmann treatment to accurately forecast biases in primordial $f_{ m NL}$ measurements and to understand the full implications for upcoming CMB surveys.

Abstract

The perturbations in the electron number density during recombination contributes to the Cosmic Microwave Background bispectrum through second order terms. Perturbations in the electron density can be a factor of ~5 larger than the baryon density fluctuations on large scales as shown in the calculations by Novosyadlyj. This raises the possibility that the contribution to bispectrum arising from perturbations in the optical depth may be non-negligible. We calculate this bispectrum and find it to peak for squeezed triangles and of peak amplitude of the order of primordial non-Gaussianity of local type with fNL of 0.05 ~ -1 depending on the l-modes being considered. This is because the shape of the bispectrum is different from the primordial one although it peaks for squeezed configurations, similar to the local type primordial non-Gaussianity.

Figures (9)

• Figure 1: $\beta_{\ell}(\tau)$ and $B_{\delta\Theta}^{\ell}(\tau)$ is shown as a function of $\tau$ for several values of $\ell$.
• Figure 2: $(\tau_0-\tau)^2\alpha_{\ell}(\tau)$ for several values of $\ell$ and the visibility function $g(\tau)$ as a function of conformal time $\tau$. $(\tau_0-\tau)^2\alpha_{\ell}(\tau)$ peaks earlier than $g(\tau)$.
• Figure 3: $B_{\Theta\Theta}^{\ell}(\tau)$ is shown for several values of $\ell$. Also shown are contributions from the polarization term $\Pi$, slip term $\theta_b-\theta_g$ and from all the other terms $\sum_{\ell \geq 2}\Theta^{(1)}_{\ell}$.
• Figure 4: $0.1\times \ell(\ell+1)\beta_{\ell}(\tau_{\ast})$,$0.01\times \ell(\ell+1)B^{\ell}_{\delta\Theta}(\tau_{\ast})$, $\ell(\ell+1)B^{\ell}_{\Theta\Theta}(\tau_{\ast})$ and contributions to it from polarization, slip and rest of the terms is shown as a function of multipole moments $\ell$. Some of the functions have been scaled as specified above.
• Figure 5: Absolute value of $B^{\ell_1 \ell_2 \ell_3}_{prim}$ labeled "Primordial" and $B^{\ell_1 \ell_2 \ell_3}$ labeled "Recombination" for $\ell_3=10$. Z axis is on linear scale while color plot shows the same on log scale.