Kavli Affiliate: Misao Sasaki
| First 5 Authors: Yi-Fu Cai, Xiao-Han Ma, Misao Sasaki, Dong-Gang Wang, Zihan Zhou
| Summary:
For primordial perturbations, deviations from Gaussian statistics on the tail
of the probability distribution can be associated with non-perturbative effects
of inflation. In this paper, we present some particular examples in which the
tail of the distribution becomes highly non-Gaussian although the statistics
remains almost Gaussian in the perturbative regime. We begin with an extension
of the ultra-slow-roll inflation that incorporates a transition process, where
the inflaton climbs up a tiny potential step at the end of the non-attractor
stage before it converges to the slow-roll attractor. Through this example, we
identify the key role of the off-attractor behaviour for the upward-step
transition, and then extend the analysis to another type of the transition with
two slow-roll stages connected by a tiny step. We perform both the perturbative
and non-perturbative analyses of primordial fluctuations generated around the
step in detail, and show that the tiny but nontrivial transition may affect
large perturbations in the tail of the distribution, while the perturbative
non-Gaussianity remains small. Our result indicates that the non-Gaussian tails
can have rich phenomenology which has been overlooked in conventional analyses.
We also study the implications of this non-Gaussian tail for the formation of
primordial black holes, and find that their mass fraction can be parametrically
amplified by several orders of magnitudes in comparison with the case of the
Gaussian distribution. Additionally, we also discuss a mechanism of primordial
black holes formation for this upward step inflation model by trapping the
inflaton in the bottom of the step.
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