Probing the running of primordial bispectrum and trispectrum using CMB spectral distortions

We compute the impact of the running of higher order density correlation functions on the two point functions of cosmic microwave background (CMB) spectral distortions (SDs). We show that having some level of running enhances all of the SDs by a few orders of magnitude, which might make them easier to detect. Taking a reasonable range for |n_fNL|≲1.1 and with f_{N L}=5 , we show that for a PIXIE-like experiment, the signal to noise ratio, (S /N )_i, enhances to ≲4000 and ≲10 for μ T and y T toward the upper limit of n_fNL. In addition, assuming |n_τNL|<1 and τ_{N L}=10³ , (S /N )_i increases to ≲8 ×10⁶, ≲10⁴, and ≲18 for μ μ , μ y , and y y , respectively. Therefore CMB spectral distortion can be a direct probe of running of higher order correlation functions in the near future.