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

TL;DR

This paper explores the potential of future CMB spectrometry experiments like PIXIE to detect or exclude spectral distortions and spectral index running, providing guaranteed discovery thresholds and improved parameter constraints.

Contribution

It introduces a benchmark sensitivity level for PIXIE-like experiments that guarantees detection of $$-distortions or exclusion of spectral index running, and discusses the impact on cosmological parameter measurements.

Findings

A sensitivity of about 3 times PIXIE guarantees detection or exclusion of spectral distortions.

Combining PIXIE with Planck improves measurements of spectral tilt and running.

Detection of negative running at 2 sigma is possible with 5 times PIXIE for a fiducial running of -0.01.

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 $n\geq1$ 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 $\mu_8=1.57^{+0.11}_{-0.13}$ ($68\%\,\mathrm{CL}$). This becomes $\mu_{8} = 1.28^{+0.30}_{-0.52}$ ($68\%\,\mathrm{CL}$) 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 $\alpha_\mathrm{s}\geq 0$ 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.