In a modified gravity theory, the propagation equation of gravitational waves will be presented in a nonstandard way. Therefore this tensor mode perturbation of time-space, as a complement to the scalar mode perturbation, provides a unique character distinguishing modified gravity from general relativity. To avoid the model-dependent issue, in this paper, we propose a parametrized modification to the propagation of gravitational waves. We show the effects on the angular power spectrum of cosmic microwave background radiation due to the parametrized modification and its degeneracy to the tensor mode power spectrum index n(t) and its running at. Last, we report the current status on the detection of modified gravity through the currently available cosmic observations. Our results show no significant deviation to general relativity.
National Natural Science Foundation of China 
; Fundamental Research Funds for the Central Universities
; Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences (People's Republic of China) [Y4KF101CJ1]