Future CMB ISW-Lensing bispectrum constraints on modified gravity in the
  Parameterized Post-Friedmann formalism
  We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukin
model of modified gravity within the Parameterized Post-Friedmann (PPF)
formalism for the Planck satellite experiment by performing the joint analysis
of ISW-Lensing bispectrum and CMB power spectrum. We find that, even
considering the temperature-temperature mode of CMB power spectrum only, Planck
data 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 scalar
degree of freedom) at least one order magnitude compared with WMAP. The
spectrum-bispectrum joint analysis can further improve the results by a factor
ranging from 1.14 to 5.32 depending on the specific modified gravity model. One
of our main results is that the cross-correlation between ISW-Lensing
bispectrum and power spectrum can be safely neglected when performing the joint
analysis. For simplicity, we only investigate the likelihood of one parameter
({$B_0$}) and fix all other cosmological parameters to their best-fit values in
WMAP7yr results.
