Consistency relations for large-scale structure in modified gravity and the matter bispectrum

TL;DR

This paper investigates how modified gravity theories affect large-scale structure formation, deriving conditions under which consistency relations hold or are violated, and explores the observational implications for the matter bispectrum.

Contribution

It extends perturbation theory to general scalar-tensor theories, identifying when large-scale consistency relations are valid or broken, and analyzes the impact on the matter bispectrum.

Findings

Consistency relations hold in Horndeski theories due to symmetry.

Beyond Horndeski theories violate these relations, affecting the squeezed limit.

Modification of the matter bispectrum depends only on linear theory.

Abstract

We study perturbation theory for large-scale structure in the most general scalar-tensor theories propagating a single scalar degree of freedom, which include Horndeski theories and beyond. We model the parameter space using the effective field theory of dark energy. For Horndeski theories, the gravitational field and fluid equations are invariant under a combination of time-dependent transformations of the coordinates and fields. This symmetry allows one to construct a physical adiabatic mode which fixes the perturbation-theory kernels in the squeezed limit and ensures that the well-known consistency relations for large-scale structure, originally derived in general relativity, hold in modified gravity as well. For theories beyond Horndeski, instead, one generally cannot construct such an adiabatic mode. Because of this, the perturbation-theory kernels are modified in the squeezed limit and the consistency relations for large-scale structure do not hold. We show, however, that the modification of the squeezed limit depends only on the linear theory. We investigate the observational consequences of this violation by computing the matter bispectrum. In the squeezed limit, the largest effect is expected when considering the cross-correlation between different tracers. Moreover, the individual contributions to the 1-loop matter power spectrum do not cancel in the infrared limit of the momentum integral, modifying the power spectrum on non-linear scales.