CMB lensing bispectrum from nonlinear growth of the large scale structure

We discuss detectability of the nonlinear growth of the large-scale structure in the cosmic microwave background (CMB) lensing. The lensing signals involved in the CMB fluctuations have been measured from multiple CMB experiments, such as Atacama Cosmology Telescope (ACT), Planck, POLARBEAR, and South Pole Telescope (SPT). The reconstructed CMB lensing signals are useful to constrain cosmology via their angular power spectrum, while detectability and cosmological application of their bispectrum induced by the nonlinear evolution are not well studied. Extending the analytic estimate of the galaxy lensing bispectrum presented by Takada and Jain (2004) to the CMB case, we show that even near term CMB experiments such as Advanced ACT, Simons Array and SPT3G could detect the CMB lensing bispectrum induced by the nonlinear growth of the large-scale structure. In the case of the CMB Stage-IV, we find that the lensing bispectrum is detectable at $\gtrsim 50\sigma$ statistical significance. This precisely measured lensing bispectrum has rich cosmological information, and could be used to constrain cosmology, e.g., the sum of the neutrino masses and the dark-energy properties.

Figure 1

The lensing bispectra with the enfolded (${\ell }_1=2{\ell }_2=2{\ell }_3$; red) and equilateral (${\ell }_1={\ell }_2={\ell }_3$; green) triangular configurations in the multipole space. The dashed lines (denoted by “tree”) show the bispectrum from the tree level prediction.

Figure 2

The contribution to the enfolded (${\ell }_1=2{\ell }_2=2{\ell }_3$) lensing bispectrum from the gravitational potential of the LSS between $z=0$ and $z_{\max }$. The black dashed line shows the full lensing bispectrum. The maximum redshift is varied from $z_{\max }=1$ to 10. For illustrative purposes, we multiply ${10}^{11}{\ell }_1$ to the lensing bispectrum.

Figure 3

Expected cumulative signal-to-noise ratios of the CMB lensing bispectrum with the S3-wide (such as Advanced ACT and Simons Array), the S3-deep (such as SPT3G) and the CMB Stage-IV. The dashed lines show the cases with the noise spectra computed from the quadratic estimator of Ref. [37].