Planck-2015 data seem to favor a large value of the lensing amplitude parameter, $A_{\mathrm{L}}=1.22\pm 0.10$, in CMB spectra. This result is in $2\sigma$ tension with the lensing reconstruction result, $A_{\mathrm{L}}^{\varphi \varphi }=0.95\pm 0.04$. In this paper, we simulate several CMB anisotropy and CMB lensing spectra based on Planck-2015 best-fit cosmological parameter values and Planck bluebook beam and noise specifications. We analyze 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 $A_{\mathrm{L}}$ 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 CMB anisotropy data from Planck with other data, such as weak lensing from CFHTLenS which favor a smaller amplitude of matter fluctuations.

• Received 27 February 2015

DOI:https://doi.org/10.1103/PhysRevD.91.123515