Effective Theory of Large-Scale Structure with Primordial Non-Gaussianity

TL;DR

The paper develops an extension of the effective-field-theory approach to large-scale structure (EFT-of-LSS) to include primordial non-Gaussianity (PNG) by deriving new operators in the effective stress tensor that arise from the squeezed-limit of the primordial bispectrum. It provides a complete classification of PNG-induced contributions by angular spin and scaling, demonstrates that the EFT remains closed under renormalization with a full basis of counterterms and noise terms, and explicitly constructs the one-loop renormalization framework for the power spectrum and bispectrum in PNG scenarios. The authors implement a numerical analysis for local, equilateral, and quasi-single-field PNG shapes, separating Gaussian and non-Gaussian contributions and showing how PNG alters nonlinear corrections on mildly nonlinear scales. The work highlights how nonlinear gravitational evolution shapes and potentially obscures primordial signatures, and lays groundwork for extracting PNG information from large-scale structure surveys through a self-consistent, renormalized EFT formalism.

Abstract

We develop the effective theory of large-scale structure for non-Gaussian initial conditions. The effective stress tensor in the dark matter equations of motion contains new operators, which originate from the squeezed limit of the primordial bispectrum. Parameterizing the squeezed limit by a scaling and an angular dependence, captures large classes of primordial non-Gaussianity. Within this parameterization, we classify the possible contributions to the effective theory. We show explicitly how all terms consistent with the symmetries arise from coarse graining the dark matter equations of motion and its initial conditions. We also demonstrate that the system is closed under renormalization and that the basis of correction terms is therefore complete. The relevant corrections to the matter power spectrum and bispectrum are computed numerically and their relative importance is discussed.

Figures (11)

• Figure 1: Solid (dashed) lines show the full (tree-level) non-Gaussian SPT contribution at $z=0$ for three representative models of primordial non-Gaussianity (see §\ref{['sec:results']} for more details).
• Figure 2: Diagrammatic representation of the one-loop power spectrum and the one-loop bispectrum for Gaussian initial conditions.
• Figure 3: Diagrammatic representation of the non-Gaussian contributions to the one-loop bispectrum. The diagrams of type II are renormalized by the same counterterms that renormalize the one-loop power spectrum.
• Figure 4: Scaling of the initial matter power spectrum. We see that in the momentum regions $[0.02,0.07]\,h {\rm Mpc}^{-1}$ and $[0.07,0.25]\,h {\rm Mpc}^{-1}$ the power spectrum is well approximated by a power law with $n\approx -0.9$ and $k_{\mathsmaller{\rm NL}}\approx 0.16\,h {\rm Mpc}^{-1}$ (red line) and $n\approx -1.5$ and $k_{\mathsmaller{\rm NL}}\approx 0.23\,h {\rm Mpc}^{-1}$ (blue line), respectively.
• Figure 5: Contributions to the bispectrum for local non-Gaussianity with $f_{\mathsmaller{\rm NL}}^{\rm local}=10$, evaluated in the equilateral configuration ( left) and for fixed $k_L \equiv 0.01\, h {\rm Mpc}^{-1}$ ( right). The definitions of $B_0^{\rm G, NG}$ and $B_c^{\rm G, NG}$ can be found in (\ref{['equ:B0']}), (\ref{['equ:BcG']}) and (\ref{['equ:BcNG']}).