  In this study, we present an analysis of the fine-tuning required in various
inflationary models in order to explain the production of Primordial Black
Holes (PBHs). We specifically examine the degree of fine-tuning necessary in
two prominent single field inflationary models: those with an inflection point
and those with step-like features in the potential. Our findings indicate that
models with step-like features generally require less fine-tuning compared to
those with an inflection point, making them more viable for consistent PBH
production. An interesting outcome of these models is that, in addition to
improved fine-tuning, they may also predict low-frequency signals that can be
detected by pulsar timing array (PTA) collaborations. Additionally, we extend
our analysis to multifield inflationary models to assess whether the
integration of additional fields can further alleviate the fine-tuning demands.
The study also explores the role of a spectator field and its impact on the
fine-tuning process. Through a comparative analysis across these models, we
evaluate their parametric sensitivities and alignment with the constraints from
Cosmic Microwave Background (CMB) observations. Our results indicate that
although mechanisms involving a spectator field can circumvent the issue of
fine-tuning parameters for PBH production, both multifield models and models
with step-like features present promising alternatives. While fine-tuning
involves multiple considerations, our primary objective is to evaluate various
inflationary models to identify the one that most naturally explains the
formation of PBHs. Hence, this study aims to the development of less
constrained inflationary scenarios that align with observational data and
support the theoretical possibility of PBH production.
