The two-loop bispectrum of large-scale structure
  The bispectrum is the leading non-Gaussian statistic in large-scale
structure, carrying valuable information on cosmology that is complementary to
the power spectrum. To access this information, we need to model the bispectrum
in the weakly non-linear regime. In this work we present the first two-loop,
i.e., next-to-next-to-leading order perturbative description of the bispectrum
within an effective field theory (EFT) framework. Using an analytic expansion
of the perturbative kernels up to $F_6$ we derive a renormalized bispectrum
that is demonstrated to be independent of the UV cutoff. We show that the EFT
parameters associated with the four independent second-order EFT operators
known from the one-loop bispectrum are sufficient to absorb the UV sensitivity
of the two-loop contributions in the double-hard region. In addition, we employ
a simplified treatment of the single-hard region, introducing one extra EFT
parameter at two-loop order. We compare our results to N-body simulations using
the realization-based grid-PT method and find good agreement within the
expected range, as well as consistent values for the EFT parameters. The
two-loop terms start to become relevant at $k\approx 0.07h~\mathrm{Mpc}^{-1}$.
The range of wavenumbers with percent-level agreement, independently of the
shape, extends from $0.08h~\mathrm{Mpc}^{-1}$ to $0.15h~\mathrm{Mpc}^{-1}$ when
going from one to two loops at $z=0$. In addition, we quantify the impact of
using exact instead of Einstein-de-Sitter kernels for the one-loop bispectrum,
and discuss in how far their impact can be absorbed into a shift of the EFT
parameters.
