Can modified gravity models reconcile the tension between CMB anisotropy
  and lensing maps in Planck-like observations?
  Planck-2015 data seem to favour a large value of the lensing amplitude
parameter, $A_{\rm L}=1.22\pm0.10$, in CMB spectra. This result is in $2\sigma$
tension with the lensing reconstruction result, $A_{\rm
L}^{\phi\phi}=0.95\pm0.04$. In this paper, we simulate several CMB anisotropy
and CMB lensing spectra based on Planck-2015 best-fit cosmological parameter
values and Planck blue book beam and noise specifications. We analyse several
modified gravity models within the effective field theory framework against
these simulations and find that models whose effective Newton constant is
enhanced can modulate the CMB anisotropy spectra in a way similar to that of
the $A_{\rm L}$ parameter. However, in order to lens the CMB anisotropies
sufficiently, like in the Planck-2015 results, the growth of matter
perturbations is substantially enhanced and gives a high $\sigma_8$ value. This
in turn proves to be problematic when combining these data to other probes,
like weak lensing from CFHTLenS, that favour a smaller amplitude of matter
fluctuations.
