$\mu$-Distortions or Running: A Guaranteed Discovery from CMB Spectrometry

Abstract

We discuss the implications of a PIXIE-like experiment, which would measure $\mu$-type spectral distortions of the CMB at a level of ${\sigma }_{\mu }=(1/n)\times 10^{-8}$, with $n\ge 1$ representing an improved sensitivity (e.g. $n=10$ corresponds to PRISM). Using Planck data and considering the six-parameter $\Lambda$CDM model, we compute the posterior for ${\mu }_8\equiv \mu \times 10^8$ and find ${\mu }_8=1.57_{-0.13}^{+0.11}$ ($68\%\mathrm{CL}$). This becomes ${\mu }_8=1.28_{-0.52}^{+0.30}$ ($68\%\mathrm{CL}$) when the running ${\alpha }_{\mathrm{s}}$ of the spectral index is included. We point out that a sensitivity of about $3\times$ PIXIE implies a guaranteed discovery: $\mu$-distortion is detected or ${\alpha }_{\mathrm{s}}\ge 0$ is excluded (both at $95\%\mathrm{CL}$ or higher). This threshold sensitivity sets a clear benchmark for CMB spectrometry. For a combined analysis of PIXIE and current Planck data, we discuss the improvement on measurements of the tilt $n_{\mathrm{s}}$ and the running ${\alpha }_{\mathrm{s}}$ and the dependence on the choice of the pivot. A fiducial running of ${\alpha }_{\mathrm{s}}=-0.01$ (close to the Planck best-fit) leads to a detection of negative running at $2\sigma$ for $5\times$ PIXIE. A fiducial running of ${\alpha }_{\mathrm{s}}=-0.02$, still compatible with Planck, requires $3\times$ PIXIE to rule out ${\alpha }_{\mathrm{s}}=0$ (at $95\%\mathrm{CL}$). We propose a convenient and compact visualization of the improving constraints on the tilt, running and tensor-to-scalar ratio.

Comments: 10+2 pages, 8 figures, 2 tables. Matches published version