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The discovery of the electromagnetic counterpart to GW170817 severelyconstrains the tensor mode propagation speed, eliminating a large model spaceof Horndeski theory. We use the cosmic microwave background data from Planckand the joint analysis of the BICEP2/Keck Array and Planck, galaxy clusteringdata from the SDSS LRG survey, BOSS baryon acoustic oscillation data, andredshift space distortion measurements to place constraints on the remainingHorndeski parameters. We evolve the Horndeski parameters as power laws withboth the amplitude and power law index free. We find a 95% CL upper bound onthe present-day coefficient of the Hubble friction term in the cosmologicalpropagation of gravitational waves is 2.38, whereas General Relativity gives 2at all times. While an enhanced friction suppresses the amplitude of thereionization bump of the primordial B-mode power spectrum at $\ell < 10$, ourresult limits the suppression to be less than 0.8%. This constraint isprimarily due to the scalar integrated Sachs-Wolfe effect in temperaturefluctuations at low multipoles.

Cosmological Constraints on Horndeski Gravity in Light of GW170817