The two-loop bispectrum of large-scale structure

Abstract

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 F6 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 twoloop 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 ≈ 0.07h Mpc −1 . The range of wavenumbers with percent-level agreement, independently of the shape, extends from 0.08h Mpc −1 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.

The Power of Locality: Primordial Non-Gaussianity at the Map Level

“…In practice, this approach usually isolates a small number of correlation functions-like the power spectrum and the bispectrum-and calculates them to some fixed order in the loop expansion. On sufficiently large scales, the errors in such a calculation can easily reach sub-percent levels [90][91][92][93][94][95]. However, since the number of independent modes decreases on large scales, the regime where perturbation theory is under the best control is also where the data has limited constraining power.…”

Snowmass white paper: Effective field theories in cosmology

“…The state-of-the-art EFT calculations that have been carried out up to now are listed in Table 1, see Refs. [90,94,99,106,[166][167][168][169][170][171][172]. These calculations must be extended to higher loop orders and higher n-point functions in order to use more observed modes in cosmological data analyses.…”

Response approach to the integrated shear 3-point correlation function: the impact of baryonic effects on small scales

“…In order to model 𝐵 3D 𝛿 in the nonlinear regime one needs to either go beyond tree-level in perturbation theory and consider the oneloop or two-loop bispectrum (Lazanu & Liguori 2018;Baldauf et al 2021), or rely on fitting formulae calibrated using N-body simulations (Scoccimarro & Couchman 2001;Gil-Marín et al 2012;Takahashi et al 2020). In their previous work on the integrated shear 3PCF, Halder et al 2021 used the bispectrum fitting formula from Gil-Marín et al 2012 (hereafter referred to as GM), which can be written as…”