Title: Large-scale Structure Bispectrum with Modal Methods, and Joint Analysis of CMB Temperature and Lensing-Reconstruction Power Spectra


First, I will present the implementation of a fast estimator for the full bispectrum of a three-dimensional particle distribution relying on a separable modal expansion of the bispectrum. The computational cost of accurate bispectrum estimation is negligible relative to the time required to run N-body simulations, so the isotropic bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated in simulations. As an application we measure the evolution of gravitational and primordial dark matter bispectra in N-body simulations with Gaussian and non-Gaussian initial conditions. The triangle dependence of the measured bispectra is compressed to about 50 coefficients, which is useful to confront theory with simulations and to treat correlations present in real data. In the nonlinear regime with $k<2h\,\mathrm{Mpc}^{-1}$, we find an excellent correlation between the measured dark matter bispectrum and a simple model based on a `constant' bispectrum plus a (nonlinear) tree-level gravitational bispectrum. In the same range for non-Gaussian simulations, we find an excellent correlation between the measured additional bispectrum and a constant model plus a (nonlinear) tree-level primordial bispectrum. We demonstrate that the constant contribution to the non-Gaussian bispectrum can be understood as a time-shift of the constant mode in the gravitational bispectrum, which is motivated by the halo model. I will also discuss modal methods to efficiently create general non-Gaussian N-body initial conditions for arbitrary primordial bispectra and a wide class of trispectra. In the second part of my talk I will address potential issues when using CMB lensing reconstructions for cosmological parameter estimation. Gravitational lensing provides a significant source of cosmological information in modern CMB parameter analyses. It is measured in both the power spectrum and trispectrum of the temperature fluctuations. These observables are often treated as independent, although as they are both determined from the same map this is impossible. We perform a rigorous analysis of the covariance between lensing power spectrum and trispectrum analyses. We find two dominant contributions coming from: (i) correlations between the disconnected noise bias in the trispectrum measurement and sample variance in the temperature power spectrum; and (ii) sample variance of the lenses themselves. The former is naturally removed when the dominant N0 Gaussian bias in the reconstructed deflection spectrum is dealt with via a partially data-dependent correction, as advocated elsewhere for other reasons. The remaining lens-cosmic-variance contribution is easily modeled but can safely be ignored for a Planck-like experiment, justifying treating the two observable spectra as independent. We also test simple likelihood approximations for the deflection power spectrum, finding that a Gaussian with a parameter-independent covariance performs well. The Planck lensing likelihood is based on the results obtained in this work.