Spectral Distortion Anisotropy from Inflation for Primordial Black Holes

Single field inflationary models that seek to greatly enhance small scale power in order to form primordial black holes predict both a squeezed bispectrum that is enhanced by this small scale power and a potentially detectable enhancement of CMB spectral distortions. Despite this combination, spectral distortion anisotropy on CMB scales remains small since the squeezed bispectrum represents an unobservable modulation of the scale rather than local amplitude for the short wavelength acoustic power that dissipates and forms the $\mu$ spectral distortion. The leading order amplitude effect comes from the local modulation of acoustic dissipation at the beginning of the $\mu$ epoch at the end of thermalization by a long wavelength mode that is correlated with CMB anisotropy itself. Compensating factors from the suppression by the square of the ratio the comoving horizon at thermalization to the smallest detectable primary CMB scales ($\sim 0.0005$) and maximal allowed enhancement of $\mu$ ($\sim 5000$) leaves a signal in the $\mu T$ cross spectrum that is still well beyond the capabilities of PIXIE or LiteBIRD due to sensitivity and resolution while remaining much larger than in single field slow roll inflation and potentially observable.