Generalized framework for testing gravity with gravitational-wave propagation. II. Constraints on Horndeski theory

TL;DR

This paper develops a model-independent numerical framework to constrain Horndeski gravity theories using gravitational wave observations, finding that many models mimicking dark energy are incompatible with GW170817 data.

Contribution

It introduces a Monte Carlo-based parameterization method to classify Horndeski models consistent with cosmic acceleration and GW observations, excluding many such models.

Findings

Many Horndeski models mimicking ΛCDM are excluded by GW170817 data.

The subclass with arbitrary functions G_4 and G_5 cannot naturally explain cosmic acceleration.

The framework provides a way to test gravity theories using gravitational wave and electromagnetic observations.

Abstract

Gravitational waves (GW) are generally affected by modification of a gravity theory during propagation in cosmological distance. We numerically perform a quantitative analysis on Horndeski theory at cosmological scale to constrain the Horndeski theory by GW observations in model-independent way. We formulate a parameterization for a numerical simulation based on the Monte Carlo method and obtain the classification of the models that agrees with cosmic accelerating expansion within observational errors of the Hubble parameter. As a result, we find that a large group of the models in the Horndeski theory that mimic cosmic expansion of ${\Lambda}$CDM model can be excluded from the simultaneous detection of a GW and its electromagnetic transient counterpart. Based on our result and the latest detection of GW170817 and GRB170817A, we conclude that the subclass of Horndeski theory including arbitrary functions $G_4$ and $G_5$ can hardly explain cosmic accelerating expansion without fine-tuning.