Primordial Black Holes in non-linear perturbation theory
  This thesis begins with a study of the origin of cosmological fluctuations
with special attention to those cases in which the non-Gaussian correlation
functions are large. The analysis shows that perturbations from an almost
massless auxiliary field generically produce large values of the non-linear
parameter f_NL. The effects of including non-Gaussian correlation functions in
the statistics of cosmological structure are explored by constructing a
non-Gaussian probability distribution function (PDF). Such PDF is derived for
the comoving curvature perturbation from first principles in the context of
quantum field theory, with n-point correlation functions as the only input. The
non-Gaussian PDF is then used to explore two important problems in the physics
of primordial black holes (PBHs): First, to compute non-Gaussian corrections to
the number of PBHs generated from the primordial curvature fluctuations. The
second application concerns new cosmological observables. The formation of PBHs
is known to depend on two main physical characteristics: the strength of the
gravitational field produced by the initial curvature inhomogeneity and the
pressure gradient at the edge of the curvature configuration. We account for
the probability of finding these configurations by using two parameters: The
amplitude of the inhomogeneity and its second radial derivative, evaluated at
the centre of the configuration. The implications of the derived probability
for the fraction of mass in the universe in the form of PBHs are discussed.
