Running the running

TL;DR

This study uses Planck satellite data to constrain the running and running of the running of the spectral index of primordial fluctuations, finding hints of a non-zero running of the running at about two standard deviations.

Contribution

It provides new constraints on the running and running of the running of the spectral index using Planck data, and explores their cosmological implications and potential for future measurements.

Findings

Hints of a non-zero running of the running at two sigma

Planck data are more compatible with standard cosmological parameters when including the running of the running

Future experiments like PIXIE could significantly improve constraints on these parameters

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 $\alpha_\mathrm{s}=0.011\pm0.010$ and $\beta_\mathrm{s}=0.027\pm0.013$ 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 $143\,\mathrm{GHz}$, $A^{PS}_{143}$, which shifts by half sigma when the running of the running is considered. We further study the cosmological implications of such preference for $\alpha_\mathrm{s},\beta_\mathrm{s}\sim0.01$ 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 $\beta_\mathrm{s}$.