Cosmological hints of modified gravity?

The recent measurements of cosmic microwave background (CMB) temperature and polarizationanisotropies made by the Planck satellite have provided impressive confirmation of theΛCDM cosmologicalmodel. However interesting hints of slight deviations fromΛCDM have been found, including a 95% C.L.preference for a“modified gravity”(MG) structure formation scenario. In this paper we confirm thepreference for a modified gravity scenario from Planck 2015 data, find that modified gravity solves the so-calledAlensanomaly in the CMB angular spectrum, and constrains the amplitude of matter densityfluctuations toσ8¼0.815þ0.032−0.048, in better agreement with weak lensing constraints. Moreover, we find alower value for the reionization optical depth ofτ¼0.0590.020(to be compared with the value ofτ¼0.0790.017obtained in the standard scenario), more consistent with recent optical and UV data. Wecheck the stability of this result by considering possible degeneracies with other parameters, including theneutrino effective number, the running of the spectral index and the amount of primordial helium. Theindication for modified gravity is still present at about 95% C.L., and could become more significant if lowervalues ofτwere to be further confirmed by future cosmological and astrophysical data. When the CMBlensing likelihood is included in the analysis the statistical significance for MG simply vanishes, indicatingalso the possibility of a systematic effect for this MG signa