Nonlinear dynamics in Horndeski gravity: a renormalized approach to effective gravitational coupling

TL;DR

This paper introduces a renormalized perturbation theory for nonlinear structure formation in Horndeski gravity, capturing both large-scale modifications and small-scale screening effects to improve cosmological predictions.

Contribution

It extends perturbative methods to Horndeski theories, defining a nonlinear effective gravitational constant that accounts for screening effects in structure formation.

Findings

Renormalized gravitational constant varies with scale and redshift.

Numerical strategies for computing the effective gravitational constant are developed.

Results improve predictions of matter power spectrum and bispectrum in modified gravity.

Abstract

This paper develops a renormalized perturbation theory framework for nonlinear structure formation in a broad class of modified gravity models that exhibit Vainshtein screening, with a focus on a viable subclass of Horndeski theories. We extend earlier perturbative methods, originally applied to DGP model, to construct a self-consistent treatment that captures both the linear modifications to gravity at large scales and the nonlinear screening effects at small scales. In the framework, the response of the gravitational potential to matter density fluctuations is characterized by renormalized propagators, leading to the definition of a nonlinear (or renormalized) effective gravitational constant. The paper details several numerical strategies to compute this renormalized gravitational constant. Numerical examples illustrate how the effective gravitational constant evolves with scale and redshift. These results are key to accurately predicting cosmological observables such as the matter power spectrum and bispectrum in modified gravity scenarios.