Bias to CMB lensing measurements from the bispectrum of large-scale structure

The rapidly improving precision of measurements of gravitational lensing of the cosmic microwave background (CMB) also requires a corresponding increase in the precision of theoretical modeling. A commonly made approximation is to model the CMB deflection angle or lensing potential as a Gaussian random field. In this paper, however, we analytically quantify the influence of the non-Gaussianity of large-scale structure (LSS) lenses, arising from nonlinear structure formation, on CMB lensing measurements. In particular, evaluating the impact of the nonzero bispectrum of large-scale structure on the relevant CMB four-point correlation functions, we find that there is a bias to estimates of the CMB lensing power spectrum. For temperature-based lensing reconstruction with CMB stage III and stage IV experiments, we find that this lensing power spectrum bias is negative and is of order 1% of the signal. This corresponds to a shift of multiple standard deviations for these upcoming experiments. We caution, however, that our numerical calculation only evaluates two of the largest bias terms and, thus, only provides an approximate estimate of the full bias. We conclude that further investigation into lensing biases from nonlinear structure formation is required and that these biases should be accounted for in future lensing analyses.