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We use the recent observations of cosmic microwave background (CMB) temperature and polarization anisotropies provided by the Planck satellite experiment to place constraints on the running ₒ=dnₒ/dlogk and the running of the running ₒ=dₒ/dlogk of the spectral index nₒ of primordial scalar fluctuations. We find ₒ=0. 0110. 010 and ₒ=0. 0270. 013 at 68% C. L. , suggesting the presence of a running of the running at the level of two standard deviations. We find no significant correlation between ₒ and foregrounds parameters, with the exception of the point sources amplitude at 143 GHz, A₁₄₃^PS, which shifts by a half-sigma when the running of the running is considered. We further study the cosmological implications of such a preference for ₒ, ₒ0. 01 by including in the analysis the lensing amplitude A₋, the curvature parameter ₊, and the sum of neutrino masses m_. We find that when the running of the running is considered Planck data are more compatible with the standard expectations of A₋=1 and ₊=0 but still hint at possible deviations. The indication for ₒ>0 survives at two standard deviations when external data sets such as baryon acoustic oscillation surverys and CFHTLenS are included in the analysis and persists at 1. 7 standard deviations when CMB lensing is considered. We discuss the possibility of constraining ₒ with current and future measurements of CMB spectral distortions, showing that an experiment like PIXIE could provide strong constraints on ₒ and ₒ.
Cabass et al. (Wed,) studied this question.