Primordial black holes and local non-Gaussianity in canonical inflation

Abstract

Primordial black holes (PBHs) cannot be produced abundantly enough to be the dark matter in canonical single-field inflation under slow roll. This conclusion is robust to local non-Gaussian correlations between long-and short-wavelength curvature modes, which we show have no effect in slow roll on local primordial black hole abundances. For the prototypical model which evades this no go, ultra-slow roll (USR), these squeezed non-Gaussian correlations have at most an order unity effect on the variance of PBH-producing curvature fluctuations for models that would otherwise fail to form sufficient PBHs. Moreover, the transition out of USR, which is necessary for a successful model, suppresses even this small enhancement unless it causes a large increase in the inflaton kinetic energy in a fraction of an e-fold, which we call a large and fast transition. Along the way we apply the in-in formalism, the δN formalism, and gauge transformations to compute non-Gaussianities and illuminate different aspects of the physical origin of these results. Local non-Gaussianity in the squeezed limit does not weaken the Gaussian conclusion that PBHs as dark matter in canonical single-field inflation require a complicated and fine-tuned potential shape with an epoch where slow roll is transiently violated.

Constant roll and primordial black holes

“…First, it would be interesting to investigate non-Gaussianity of the three-stage CR model. While, a priori, one may expect that it has a negligible impact on the PBH production (as is the case within USR, see [49]), a dedicated study would be appropriate. It would be also interesting to replace the transitions in the potential by a multi-field model, such as curvaton scenario, capable of generating the desired power spectrum on every scale of interest.…”

From primordial black holes abundance to primordial curvature power spectrum (and back)

“…In fact, primordial non-Gaussianities affect both CPBH formation and abundance and are generally expected to be produced in many of the proposed models for CPBHs generation, see e.g., Refs. [173][174][175][176][177][178][179]. While it has been tested that at cosmological scales initial conditions are very close to be Gaussian [148,[180][181][182][183], this has not been verified at very small scales, i.e., for the range of scales k 10 5 Mpc −1 relevant for CPBH formation.…”

Primordial black hole tower: Dark matter, earth-mass, and LIGO black holes

“…n S − 1 = d log P R d log k , and its running α = dn S d log k are slow-roll suppressed in the simplest single-field slow-roll inflation, prohibiting such an amplification. This difficulty has been reported even beyond the slow-roll approximation [57,58]. On the other hand, if one allows two/multiple phases of inflation during the last 50-60 efolds, the PBH scale can be free from the CMB scale constraint and such an amplification can be realized much more easily.…”