New Window on Primordial Non-Gaussianity

We know very little about primordial curvature perturbations on scales smaller than about a Mpc. Measurements of the μ distortion of the cosmic microwave background spectrum provide the unique opportunity to probe these scales over the unexplored range from 50 to 10⁴ Mpc^-1. This is a very clean probe, in that it relies only on well understood linear evolution. Also, just the information about the low multipoles (l~100) of μ is necessary. We point out that correlations between μ distortion and temperature anisotropies can be used to test Gaussianity at these very small scales. In particular the μT two-point correlation is proportional to the very squeezed limit of the primordial bispectrum and hence measures fNLˡᵒᶜ, while μμ is proportional to the primordial trispectrum and measures τNL. We present a Fisher matrix forecast of the observational constraints on fNLˡᵒᶜ and stress that a cosmic variance limited experiment could in principle reach ΔfNLˡᵒᶜ~O(10^-3).