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

Many inflation models predict that primordial density perturbations have a nonzero three-point correlation function, or bispectrum in Fourier space. Of the several possibilities for this bispectrum, the most common is the local-model bispectrum, which can be described as a spatial modulation of the small-scale (large-wavenumber) power spectrum by long-wavelength density fluctuations. While the local model predicts this spatial modulation to be scale independent, many variants have some scale dependence. Here we note that this scale dependence can be probed with measurements of frequency-spectrum distortions in the cosmic microwave background (CMB), in particular, highlighting Compton-$y$ distortions. Dissipation of primordial perturbations with wavenumbers $50{\mathrm{Mpc}}^{-1}\lesssim k\lesssim {10}^4{\mathrm{Mpc}}^{-1}$ gives rise to chemical-potential ($\mu$) distortions, while dissipation of those with wavenumbers $1{\mathrm{Mpc}}^{-1}\lesssim k\lesssim 50{\mathrm{Mpc}}^{-1}$ gives rise to Compton-$y$ distortions. With local-model non-Gaussianity, the distortions induced by this dissipation can be distinguished from those due to other sources via their cross correlation with the CMB temperature $T$. We show that the relative strengths of the $\mu T$ and $yT$ correlations thus probe the scale dependence of non-Gaussianity and estimate the magnitude of possible signals relative to the sensitivities of future experiments. We discuss the complementarity of these measurements with other probes of squeezed-limit non-Gaussianity.

Figure 1

The different $k$-space windows responsible for different observables. The CMB anisotropies are visible at $k\lesssim 0.1{\mathrm{Mpc}}^{-1}$, where the small-scale cut-off is introduced by Silk damping. Compton-$y$ distortions are formed by the damping of modes with $1{\mathrm{Mpc}}^{-1}\lesssim k\lesssim 50{\mathrm{Mpc}}^{-1}$, while $\mu$ distortions are created by modes with $50{\mathrm{Mpc}}^{-1}\lesssim k\lesssim {10}^4{\mathrm{Mpc}}^{-1}$. Additional large-scale temperature power can be created by modes at ${10}^4{\mathrm{Mpc}}^{-1}\lesssim k$ [48]. Those with ${10}^4{\mathrm{Mpc}}^{-1}\lesssim k\lesssim {10}^5{\mathrm{Mpc}}^{-1}$ can be constrained using the primordial helium abundance [46, 47], while modes with ${10}^5{\mathrm{Mpc}}^{-1}\lesssim k$ are erased before neutrino decoupling, and thus would only lead to additional large-scale temperature fluctuations.