Spectral distortion anisotropies from single-field inflation

Distortions of the Cosmic Microwave Background energy spectrum of the $\mu$ type are sensitive to the primordial power spectrum through the dissipation of curvature perturbations on scales $k\simeq 50$ - $10^4\,\mathrm{Mpc}^{-1}$. 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 $\mu T$ 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 $k^2/{\cal H}_f^2$, where ${\cal H}_f\simeq 10^{-1}\,{\rm Mpc}^{-1}$ is the Hubble radius at the end of the $\mu$-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 $\mu$ distortions as the ultimate probe of local primordial non-Gaussianity.