We constrain f ( R ) and chameleon-type modified gravity in the framework of the Berstchinger-Zukin parametrization using the recent released Planck data , including both CMB temperature power spectrum and lensing potential power spectrum .
Some other external data sets are included , such as baryon acoustic oscillations ( BAO ) measurements from the 6dFGS , SDSS DR7 and BOSS DR9 surveys , Hubble Space Telescope ( HST ) H _ { 0 } measurement and supernovae from Union2.1 compilation .
We also use WMAP9yr data for consistency check and comparison .
For f ( R ) gravity , WMAP9yr results can only give quite a loose constraint on the modified gravity parameter B _ { 0 } , which is related to the present value of the Compton wavelength of the extra scalar degree of freedom , B _ { 0 } < 3.37 at 95 \% { C . L . } We demonstrate that this constraint mainly comes from the late Integrated Sachs-Wolfe effect .
With only Planck CMB temperature power-spectrum data , we can improve the WMAP9yr result by a factor 3.7 ( B _ { 0 } < 0.91 at 95 \% { C . L . } ) .
If the Planck lensing potential power-spectrum data are also taken into account , the constraint can be further strenghtened by a factor 5.1 ( B _ { 0 } < 0.18 at 95 \% { C . L . } ) .
This major improvement mainly comes from the small-scale lensing signal .
Furthermore , BAO , HST and supernovae data could slightly improve the B _ { 0 } bound ( B _ { 0 } < 0.12 at 95 \% { C . L . } ) .
For the chameleon-type model , we find that the data set which we used can not constrain the Compton wavelength B _ { 0 } and the potential index s of chameleon field , but can give a tight constraint on the parameter \beta _ { 1 } = 1.043 ^ { +0.163 } _ { -0.104 } at 95 \% { C . L . } ( \beta _ { 1 } = 1 in general relativity ) , which accounts for the non-minimal coupling between the chameleon field and the matter component .
In addition , we find that both modified gravity models we considered favor a relatively higher Hubble parameter than the concordance \Lambda CDM model in general relativity .