mu-distortions or running: A guaranteed discovery from CMB spectrometry

We discuss the implications of a PIXIE-like experiment, which would measure μ -type spectral dis- tortions of the CMB at a level of σ μ = (1 /n)×10−8, with n≥1 representing an improved sensitivity (e.g. n= 10 corresponds to PRISM). Using Planck data and considering the six-parameter ΛCDM model, we compute the posterior for μ 8 ≡ μ×10 8 nd find μ 8 = 1 57 +0 .11 − . 13 (68% CL). This becomes μ 8 = 1 .28 +0.30 −0 .52 (68% CL) when the running α s of the spectral index is included. We point out that a sensitivity of about 3 × PIXIE implies a guaranteed discovery : μ -distortion is detected or α s ≥ 0 is excluded (both at 95% 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 snd the running α s nd the dependence on the choice of the pivot. A fiducial running of α s = −0 .01 (close to the Planck best-fit) leads to a detection of negative running at 2 σ for 5 × PIXIE. A fiducial running of α s = − 0. 02, still compatible with Planck , requires 3 × PIXIE to rule out α s = 0 (at 95% CL). We propose a convenient and compact visualization of the improving constraints on the tilt, running and tensor-to-scalar ratio