Primordial trispectra and CMB spectral distortions

We study the TTμ bispectrum, generated by correlations between Cosmic Microwave Background temperature (T) anisotropies and chemical potential (μ) distortions, and we analyze its dependence on primordial local trispectrum parameters gNL and τNL. We cross-check our results by comparing the full bispectrum calculation with the expectations from a general physical argument, based on predicting the shape of μ-T correlations from the couplings between short and long perturbation modes induced by primordial non-Gaussianity. We show that both gNL and τNL-parts of the primordial trispectrum source a non-vanishing TTμ signal, contrary to the μμ auto-correlation function, which is sensitive only to the τNL-component. A simple Fisher matrix-based forecast shows that a futuristic, cosmic-variance dominated experiment could in principle detect gNL∼0.4 and τNL∼40 using TTμ.