μ distortions or running: A guaranteed discovery from CMB spectrometry

We discuss the implications of a PIXIE-like experiment, which would measure mu-type spectral distortions of the cosmic microwave background (CMB) at a level of sigma(mu) = (1/n) x 10(-8), with n >= 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) = mu x 108 and find mu 8 = 1.57(-0.13)(+0.11) (68% C.L.). This becomes mu(8) = 1.28(-0.52)(+0.30) (68% C.L.) when the running as of the spectral index is included. We point out that a sensitivity of about 3 x PIXIE implies a guaranteed discovery: mu distortion is detected or as = 0 is excluded (both at 95% C.L. 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(s) and the running as and the dependence on the choice of the pivot. A fiducial running of alpha(s) = -0.01 (close to the Planck best fit) leads to a detection of negative running at 2 sigma for 5 x PIXIE. A fiducial running of alpha(s) = -0.02, still compatible with Planck, requires 3 x PIXIE to rule out alpha(s) x 0 (at 95% C.L.). We propose a convenient and compact visualization of the improving constraints on the tilt, running and tensor-to-scalar ratio.