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CMB 3-point functions generated by non-linearities at recombination

Paolo Creminelli, Matias Zaldarriaga

Abstract

We study the 3-point functions generated at recombination in the squeezed triangle limit, when one mode has a wavelength much larger than the other two and is outside the horizon. The presence of the long wavelength mode cannot change the physics inside the horizon but modifies how a late time observer sees the anisotropies. The effect of the long wavelength mode can be divided into a redefinition of time and spatial scales, a Shapiro time delay and gravitational lensing. The separation is gauge dependent but helps develop intuition. We show that the resulting 3-point function corresponds to an f_NL < 1 and that its shape is different from that created by the f_NL (or local) model.

CMB 3-point functions generated by non-linearities at recombination

Abstract

We study the 3-point functions generated at recombination in the squeezed triangle limit, when one mode has a wavelength much larger than the other two and is outside the horizon. The presence of the long wavelength mode cannot change the physics inside the horizon but modifies how a late time observer sees the anisotropies. The effect of the long wavelength mode can be divided into a redefinition of time and spatial scales, a Shapiro time delay and gravitational lensing. The separation is gauge dependent but helps develop intuition. We show that the resulting 3-point function corresponds to an f_NL < 1 and that its shape is different from that created by the f_NL (or local) model.

Paper Structure

This paper contains 5 sections, 42 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The effect of the background wave
  3. The 3-point function
  4. Polarization 3-point functions.
  5. Conclusions

Figures (4)

  • Figure 1: Signal to noise as a function of the maximum $l$ for an ideal, cosmic variance limited experiment. Dashed line: space redefinition effect. Continuous thin line: isotropic lensing effect. Thick line: total effect. We see that the total signal to noise is smaller than the individual contributions as the two effects partially cancel. The parameters of the cosmological model we used were: $\Omega_b=0.045$, $\Omega_c=0.255$, $\Omega_\Lambda=0.7$, $h=0.7$ and $\sigma_8=0.85$.
  • Figure 2: Signal to noise for the anisotropic lensing contribution (thick line) compared to the sum of the isotropic contributions (thin line) as a function of the maximum $l$ for an ideal, cosmic variance limited experiment. The anisotropic effect has a bigger signal to noise. Cosmological parameters are the same as in the previous figures.
  • Figure 3: Signal to noise for the TTE (continuous line) and TEE (dashed line) correlators as a function of the maximum $l$ for an ideal, cosmic variance limited experiment. Cosmological parameters are the same as in the previous figures.
  • Figure 4: Signal to noise for the TTB (continuous line) and TEB (dashed line) correlators as a function of the maximum $l$ for an ideal, cosmic variance limited experiment. Cosmological parameters are the same as in the previous figures.