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 nonlinear 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 perturbation theory 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 wave numbers with percent-level agreement, independently of the shape, extends from $0.08$ 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.

• Received 11 November 2021
• Accepted 24 November 2021

DOI:https://doi.org/10.1103/PhysRevD.104.123551