Supermassive black holes formed by direct collapse of inflationary perturbations

We propose a mechanism of producing a new type of primordial perturbations that collapse to primordial black holes, whose mass can be as large as necessary for them to grow to the supermassive black holes observed at high redshifts, without contradicting Cosmic Background Explorer/Far Infrared Absolute Spectrophotometer (COBE/FIRAS) upper limits on cosmic microwave background (CMB) spectral distortions. In our model, the observable Universe consists of two kinds of many small patches which experienced different expansion histories during inflation. Primordial perturbations large enough to form primordial black holes are realized on patches that experienced more Hubble expansion than the others. By making these patches the minor component, the rarity of supermassive black holes can be explained. On the other hand, most regions of the Universe experienced the standard history and, hence, only have standard-almost-scale-invariant adiabatic perturbations confirmed by observations of CMB or large-scale structures of the Universe. Thus, our mechanism can evade the constraint from the nondetection of the CMB distortion set by the COBE/FIRAS measurement. Our model predicts the existence of supermassive black holes even at redshifts much higher than those observed. Hence, our model can be tested by future observations peeking into the higher-redshift Universe.