Primordial Black Holes in non-linear perturbation theory

TL;DR

This thesis investigates the impact of non-Gaussian primordial fluctuations on the formation of primordial black holes, deriving a non-Gaussian PDF from quantum field theory to improve predictions of PBH abundance.

Contribution

It introduces a first-principles non-Gaussian PDF for curvature perturbations and applies it to refine PBH formation estimates considering non-Gaussian effects.

Findings

Non-Gaussian correlations can significantly alter PBH abundance estimates.

The derived PDF enables more accurate modeling of primordial fluctuations.

Implications for cosmological observables related to PBHs are discussed.

Abstract

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.