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 commmon is the local-model bispectrum, whi
ch 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 $50,{rm Mpc}^{-1} lesssim k lesssim 10^4,{rm Mpc}^{-1}$ give rise to chemical-potential ($mu$) distortions, while those with wavenumbers $1,{rm Mpc}^{-1} lesssim k lesssim 50,{rm Mpc}^{-1}$ give 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 sensitivities of future experiments. We discuss the complementarity of these measurements with other probes of squeezed-limit non-Gaussianity.
Gauge-flation is a recently proposed model in which inflation is driven solely by a non-Abelian gauge field thanks to a specific higher order derivative operator. The nature of the operator is such that it does not introduce ghosts. We compute the co
smological scalar and tensor perturbations for this model, improving over an existing computation. We then confront these results with the Planck data. The model is characterized by the quantity gamma = (g^2 Q^2)/H^2 (where g is the gauge coupling constant, Q the vector vev, and H the Hubble rate). For gamma < 2, the scalar perturbations show a strong tachyonic instability. In the stable region, the scalar power spectrum n_s is too low at small gamma, while the tensor-to-scalar ratio r is too high at large gamma. No value of gamma leads to acceptable values for n_s and r, and so the model is ruled out by the CMB data. The same behavior with gamma was obtained in Chromo-natural inflation, a model in which inflation is driven by a pseudo-scalar coupled to a non-Abelian gauge field. When the pseudo-scalar can be integrated out, one recovers the model of Gauge-flation plus corrections. It was shown that this identification is very accurate at the background level, but differences emerged in the literature concerning the perturbations of the two models. On the contrary, our results show that the analogy between the two models continues to be accurate also at the perturbative level.
