Cosmological Angular Trispectra and Non-Gaussian Covariance
  Angular cosmological correlators are infamously difficult to compute due to
the highly oscillatory nature of the projection integrals. Motivated by recent
development on analytic approaches to cosmological perturbation theory, in this
paper we present an efficient method for computing cosmological four-point
correlations in angular space, generalizing previous works on lower-point
functions. This builds on the FFTLog algorithm that approximates the matter
power spectrum as a sum over power-law functions, which makes certain momentum
integrals analytically solvable. The computational complexity is drastically
reduced for correlators in a "separable" form---we define a suitable notion of
separability for cosmological trispectra, and derive formulas for angular
correlators of different separability classes. As an application of our
formalism, we compute the angular galaxy trispectrum at tree level, with and
without primordial non-Gaussianity. This includes effects of redshift space
distortion and bias parameters up to cubic order. We also compute the
non-Gaussian covariance of the angular matter power spectrum due to the
connected four-point function, beyond the Limber approximation. We demonstrate
that, in contrast to the standard lore, the Limber approximation can fail for
the non-Gaussian covariance computation even for large multipoles.
