Spectral distortion anisotropies from single-field inflation

Distortions of the Cosmic Microwave Background energy spectrum of the μ type are sensitive to the primordial power spectrum through the dissipation of curvature perturbations on scales k∼ 50-10⁴ Mpc^-1. Their angular correlation with large-scale temperature anisotropies is then sensitive to the squeezed limit of the primordial bispectrum. For inflationary models obeying the single-field consistency relation, we show that the observed μ T angular correlation that would correspond to the local shape vanishes exactly. All leading non-primordial contributions, including all non-linear production and projection effects, are of the "equilateral shape", namely suppressed by k²/_f ², where _f∼Mpc^-1 is the Hubble radius at the end of the μ-era. Therefore, these non-primordial contributions are orthogonal to a potential local primordial signal (e.g. from multi-field inflation). Moreover, they are very small in amplitude. Our results strengthen the position of μ distortions as the ultimate probe of local primordial non-Gaussianity.