Cosmological Hints of Modified Gravity ?

The recent measurements of Cosmic Microwave Background temperature and polarization anisotropies made by the Planck satellite have provided impressive confirmation of the $\Lambda$CDM cosmological model. However interesting hints of slight deviations from $\Lambda$CDM have been found, including a $95 \%$ c.l. preference for a "modified gravity" structure formation scenario. In this paper we confirm the preference for a modified gravity scenario from Planck 2015 data, find that modified gravity solves the so-called $A_{lens}$ anomaly in the CMB angular spectrum, and constrains the amplitude of matter density fluctuations to $\sigma_8=0.815_{-0.048}^{+0.032}$, in better agreement with weak lensing constraints. Moreover, we find a lower value for the reionization optical depth of $\tau=0.059\pm0.020$ (to be compared with the value of $\tau= 0.079 \pm 0.017$ obtained in the standard scenario), more consistent with recent optical and UV data. We check the stability of this result by considering possible degeneracies with other parameters, including the neutrino effective number, the running of the spectral index and the amount of primordial helium. The indication for modified gravity is still present at about $95\%$ c.l., and could become more significant if lower values of $\tau$ were to be further confirmed by future cosmological and astrophysical data.