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Many inflation models predict that primordial density perturbations have anonzero three-point correlation function, or bispectrum in Fourier space. Ofthe several possibilities for this bispectrum, the most commmon is thelocal-model bispectrum, which can be described as a spatial modulation of thesmall-scale (large-wavenumber) power spectrum by long-wavelength densityfluctuations. While the local model predicts this spatial modulation to bescale-independent, many variants have some scale-dependence. Here we note thatthis scale dependence can be probed with measurements of frequency-spectrumdistortions in the cosmic microwave background (CMB), in particularhighlighting Compton-$y$ distortions. Dissipation of primordial perturbationswith wavenumbers $50\,{\rm Mpc}^{-1} \lesssim k \lesssim 10^4\,{\rm Mpc}^{-1}$give rise to chemical-potential ($\mu$) distortions, while those withwavenumbers $1\,{\rm Mpc}^{-1} \lesssim k \lesssim 50\,{\rm Mpc}^{-1}$ giverise to Compton-$y$ distortions. With local-model non-Gaussianity, thedistortions induced by this dissipation can be distinguished from those due toother sources via their cross-correlation with the CMB temperature $T$. We showthat the relative strengths of the $\mu T$ and $yT$ correlations thus probe thescale-dependence of non-Gaussianity and estimate the magnitude of possiblesignals relative to sensitivities of future experiments. We discuss thecomplementarity of these measurements with other probes of squeezed-limitnon-Gaussianity.

Probing the scale dependence of non-Gaussianity with spectral distortions of the cosmic microwave background