Renormalized Perturbation Theory at Field-level: the LSS bootstrap in GridSPT

TL;DR

This paper develops a renormalized perturbation theory framework at the field level for large-scale structure, enabling precise, model-independent cosmological inference beyond standard models by addressing UV cutoff dependence and incorporating counterterms.

Contribution

It introduces a Wilsonian perturbative approach with renormalization for grid-based LSS analysis, extending GridSPT to include bootstrap parameters and higher-order corrections.

Findings

Cutoff-independent predictions achieved with counterterms

Validated at third- and fifth-order perturbation theory

Higher-derivative terms are crucial for unbiased parameter estimation

Abstract

We present a first step toward field-level cosmological inference beyond the standard $\Lambda$CDM model, focusing on optimizing precision tests in the nonlinear regime of large-scale structure (LSS). As an illustrative case, we study the model-independent ``bootstrap'' coefficient of the second-order perturbation theory (PT) kernel for matter in real space, which we use as a proxy for new physics effects in the nonlinear sector. We discuss in details the ultraviolet (UV) cutoff dependence induced by discretizing fields on a grid, which requires proper renormalization to eliminate grid artifacts. We formulate a Wilsonian perturbative framework in which the evolution from a UV theory defined at a high cutoff $\Lambda_\text{uv}$ down to lower cutoffs is computed analytically, even beyond the validity of a derivative expansion. Within this framework, we develop an extended version of the GridSPT code incorporating the bootstrap parameterization and demonstrate how cutoff-independent predictions can be achieved through the inclusion of appropriate counterterms. We validate our approach at third- and fifth-order in PT, emphasizing the importance of higher-derivative contributions for unbiased parameter extraction. Our framework is readily extendable to biased tracers and redshift-space distortions.