Running the running

Abstract

We use the recent observations of Cosmic Microwave Background temperature and polarization anisotropies provided by the Planck satellite experiment to place constraints on the running ${\alpha }_{\mathrm{s}}=\mathrm{d}{n}_{\mathrm{s}}/\mathrm{d}\log k$ and the running of the running ${\beta }_{\mathrm{s}}=\mathrm{d}{\alpha }_{\mathrm{s}}/\mathrm{d}\log k$ of the spectral index $n_{\mathrm{s}}$ of primordial scalar fluctuations. We find ${\alpha }_{\mathrm{s}}=0.011\pm 0.010$ and ${\beta }_{\mathrm{s}}=0.027\pm 0.013$ at $68\%\mathrm{CL}$, suggesting the presence of a running of the running at the level of two standard deviations. We find no significant correlation between ${\beta }_{\mathrm{s}}$ and foregrounds parameters, with the exception of the point sources amplitude at $143\mathrm{GHz}$, $A_{143}^{PS}$, which shifts by half sigma when the running of the running is considered. We further study the cosmological implications of such preference for ${\alpha }_{\mathrm{s}},{\beta }_{\mathrm{s}}\sim 0.01$ by including in the analysis the lensing amplitude $A_L$, the curvature parameter ${\Omega }_k$, and the sum of neutrino masses $\sum m_{\nu }$. We find that when the running of the running is considered, Planck data are more compatible with the standard expectations of $A_L=1$ and ${\Omega }_k=0$ but still hint at possible deviations. The indication for ${\beta }_{\mathrm{s}}>0$ survives at two standard deviations when external datasets such as BAO and CFHTLenS are included in the analysis, and persists at $\sim 1.7$ standard deviations when CMB lensing is considered. We discuss the possibility of constraining ${\beta }_{\mathrm{s}}$ with current and future measurements of CMB spectral distortions, showing that an experiment like PIXIE could provide strong constraints on ${\alpha }_{\mathrm{s}}$ and ${\beta }_{\mathrm{s}}$.

10+1 pages, 9 figures, 10 tables. Matches published version

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