Signatures of Horndeski gravity on the Dark Matter Bispectrum

TL;DR

This paper investigates how Horndeski gravity models influence the dark matter bispectrum, finding that deviations are generally small unless the theory significantly differs from General Relativity, which could indicate exotic physics.

Contribution

It provides a detailed analysis of second-order matter perturbations in Horndeski models and assesses their impact on the dark matter bispectrum, connecting deviations to potential new physics.

Findings

Large bispectrum deviations imply significant departures from GR or exotic gravity theories.

Most Horndeski models consistent with GR's linear growth rate show negligible bispectrum deviations.

Observation of large bispectrum deviations could signal new physics beyond standard gravity theories.

Abstract

We present a detailed study of second-order matter perturbations for the general Horn- deski class of models. Being the most general scalar-tensor theory having second-order equations of motion, it includes many known gravity and dark energy theories and General Relativity with a cosmological constant as a specific case. This enables us to estimate the leading order dark matter bispectrum generated at late-times by gravitational instability. We parametrize the evolution of the first and second-order equations of motion as proposed by Bellini and Sawicki (2014), where the free functions of the theory are assumed to be proportional to the dark energy density. We show that it is unnatural to have large 10% ( 1%) deviations of the bispectrum introducing even larger ~ 30% (~ 5%) deviations in the linear growth rate. Considering that measurements of the linear growth rate have much higher signal-to-noise than bispectrum measurements, this indicates that for Horndeski models which reproduce the expansion history and the linear growth rate as predicted by GR the dark matter bispectrum kernel can be effectively modelled as the standard GR one. On the other hand, an observation of a large bispectrum deviation that can not be explained in terms of bias would imply either that the evolution of perturbations is strongly different than the evolution predicted by GR or that the theory of gravity is exotic (e.g., breaks the weak equivalence principle) and/or fine-tuned.