Constraining Palatini-Horndeski theory with gravitational waves after GW170817

TL;DR

This paper constrains the parameter space of Palatini-Horndeski gravity using gravitational wave speed measurements post-GW170817, showing that only a specific subclass of actions remains viable under the speed-of-light condition.

Contribution

It identifies the subset of Palatini-Horndeski theories consistent with gravitational wave speed constraints after GW170817.

Findings

Only a specific form of the action remains compatible with gravitational wave speed constraints.

The tensor gravitational wave speed must equal the speed of light in the viable theories.

The viable theories are characterized by a particular action form involving functions K, G3, and G4.

Abstract

In this paper, we investigate the possible parameter space of Palatini-Horndeski theory with gravitational waves in a spatially flat Universe. We find that if the theory satisfies the following condition: in any spatially flat cosmological background, the tensor gravitational wave speed is the speed of light $c$, then only $S = \int d^4x \sqrt{-g} \big[K(\phi,X)-G_{3}(\phi,X){\tilde{\Box}}\phi+G_{4}(\phi)\tilde{R}\big]$ is left as the possible action in Palatini-Horndeski theory.