Cosmological Constraints on Horndeski Gravity in Light of GW170817

Abstract: The discovery of the electromagnetic counterpart to GW170817 severely constrains the tensor mode propagation speed, eliminating a large model space of Horndeski theory. We use the cosmic microwave background data from Planck and the joint analysis of the BICEP2/Keck Array and Planck, galaxy clustering data from the SDSS LRG survey, BOSS baryon acoustic oscillation data, and redshift space distortion measurements to place constraints on the remaining Horndeski parameters. We evolve the Horndeski parameters as power laws with both the amplitude and power law index free. We find a 95% CL upper bound on the present-day coefficient of the Hubble friction term in the cosmological propagation of gravitational waves is 2.38, whereas General Relativity gives 2 at all times. While an enhanced friction suppresses the amplitude of the reionization bump of the primordial B-mode power spectrum at $\ell < 10$, our result limits the suppression to be less than 0.8%. This constraint is primarily due to the scalar integrated Sachs-Wolfe effect in temperature fluctuations at low multipoles.