Forecasts for CMB μ and i-type spectral distortion constraints on the primordial power spectrum on scales8≲k≲104 Mpc−1 with the future Pixie-like experiments

Abstract

Silk damping at redshifts 1.5 × 104≲z≲2 × 106erases CMB anisotropies on scales corresponding to the comovingwavenumbers 8≲k≲104 Mpc−1 (105≲ℓ≲108). This dissipatedenergy is gained by the CMB monopole, creating distortions from a blackbodyin the CMB spectrum of the μ-type and the i-type. Westudy, using Fisher matrices, the constraints we can get from measurementsof these spectral distortions on the primordial powerspectrum from future experiments such as Pixie, and how theseconstraints change as we change the frequency resolution and the sensitivity of the experiment. We show that the additionalinformation in the shape of the i-type distortions, in combination withthe μ-type distortions, allows us to break thedegeneracy between the amplitude and the spectral index of the powerspectrum on these scales and leads to much tighter constraints. We quantify the information contained inboth the μ-type distortions and the i-type distortions taking intoaccount the partial degeneracy with the y-type distortions and thetemperature of the blackbody part of the CMB. We also calculate theconstraints possible on the primordial power spectrum when the spectraldistortion information is combined with the CMB anisotropies measured bythe WMAP, SPT, ACT and Planck experiments.