Primordial trispectra and CMB spectral distortions

We study the TT mu bispectrum, generated by correlations between Cosmic Microwave Background temperature (T) anisotropies and chemical potential (mu) distortions, and we analyze its dependence on primordial local trispectrum parameters g(NL) and tau(NL). 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 mu-T correlations from the couplings between short and long perturbation modes induced by primordial non-Gaussianity. We show that both g(NL) and tau(NL)-parts of the primordial trispectrum source a non-vanishing TT mu signal, contrary to the mu mu auto-correlation function, which is sensitive only to the tau(NL)-component. A simple Fisher matrix-based forecast shows that a futuristic, cosmic-variance dominated experiment could in principle detect g(NL) similar to 0.4 and tau(NL) similar to 40 using TT mu.