Matter bispectrum beyond Horndeski

TL;DR

This paper investigates how beyond Horndeski theories modify the matter bispectrum in large scale structure, revealing unique effects on folded triangle configurations that are absent in standard Horndeski models.

Contribution

It derives the second-order matter density perturbation solutions in beyond Horndeski theories, highlighting new time-dependent coefficients affecting the bispectrum.

Findings

Beyond Horndeski introduces a new time-dependent coefficient in the second-order kernel.

This coefficient can deform the matter bispectrum at folded triangle configurations.

Such effects are not possible within standard Horndeski theories.

Abstract

The Horndeski scalar-tensor theory and its recent extensions allow nonlinear derivative interactions of the scalar degree of freedom. We study the matter bispectrum of large scale structure as a probe of these modified gravity theories, focusing in particular on the effect of the terms that newly appear in the so-called "beyond Horndeski" theories. We derive the second-order solution for the matter density perturbations and find that the interactions beyond Horndeski lead to a new time-dependent coefficient in the second-order kernel which differs in general from the standard value of general relativity and the Horndeski theory. This can deform the matter bispectrum at the folded triangle configurations ($k_1+k_2=k_3$), while it is never possible within the Horndeski theory.