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We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukinmodel of modified gravity within the Parameterized Post-Friedmann (PPF)formalism for the Planck satellite experiment by performing the joint analysisof ISW-Lensing bispectrum and CMB power spectrum. We find that, evenconsidering the temperature-temperature mode of CMB power spectrum only, Planckdata are expected to reduce the error bars on the modified gravity parameter$B_0$ (related to the present value of Compton wavelength of the extra scalardegree of freedom) at least one order magnitude compared with WMAP. Thespectrum-bispectrum joint analysis can further improve the results by a factorranging from 1.14 to 5.32 depending on the specific modified gravity model. Oneof our main results is that the cross-correlation between ISW-Lensingbispectrum and power spectrum can be safely neglected when performing the jointanalysis. For simplicity, we only investigate the likelihood of one parameter({$B_0$}) and fix all other cosmological parameters to their best-fit values inWMAP7yr results.

Future CMB ISW-Lensing bispectrum constraints on modified gravity in the Parameterized Post-Friedmann formalism