Two-loop bispectrum of large-scale structure

The bispectrumis 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 EFToperators 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 approximate to 0.07h Mpc(-1). The range of wave numbers with percent-level agreement, independently of the shape, extends from 0.08 to 0.15h 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.

Automated summary

In this work, a two-loop perturbative description of the bispectrum within an effective field theory (EFT) framework is presented, demonstrating the effectiveness of EFT parameters in absorbing UV sensitivity of two-loop contributions. The study shows good agreement with N-body simulations, with two-loop contributions becoming relevant at k approximate to 0.07h Mpc(-1), and percent-level agreement extending from 0.08 to 0.15h Mpc(-1) from one to two loops at z = 0.