Lecture notes on inflation and primordial black holes
  These lecture notes are based on those presented at the Theoretical Aspects
of Astroparticle Physics, Cosmology and Gravitation School at the Galileo
Galilee Institute in Florence in 2021, https://agenda.infn.it/event/24368/.
They aim to provide a pedagogical introduction and basic working knowledge of
single-field inflation including the ultra-slow-roll regime, where the
perturbations grow exponentially. This rapid growth is connected to the
formation of primordial black holes (PBHs), a special dark matter candidate and
probe of the initial conditions of the early universe. Although there are many
textbooks and introductory texts about inflation, to the best of our knowledge
there is no comparable introduction to ultra-slow-roll inflation. Furthermore,
given their recent surge in popularity, there are numerous research articles
and reviews on primordial black holes, however these notes aim to be more
accessible for graduate students and those brand new to the topic. Some
problems and solutions to primordial black hole-related calculations are also
included. The reader of these lecture notes should come away being able to
calculate the present-day abundance of primordial black holes produced from the
density fluctuations left over at the end of single-field inflation with an
ultra-slow-roll phase, and understand how this abundance compares with current
observational constraints.
