Primordial black holes in non-linear perturbation theory

Abstract

The thesis begins with a study of the origin of non-linear cosmological fluctuations. In particular, a class of models of multiple field inflation are considered, with specific reference 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 fNL. Next, the effects of including non-Gaussian correlation functions in the statistics of cosmological structure are explored. For this purpose, a non-Gaussian probability distribution function (PDF) for the curvature perturbationR is required. Such a PDF is derived from first principles in the context of quantum field theory, with n-point correlation functions as the only input. Under reasonable power-spectrum conditions, an explicit expression for the PDF is presented, with corrections to the Gaussian distribution from the three-point correlation function hRRRi. The method developed for the derivation of the non-Gaussian PDF is then used to explore two important problems in the physics of primordial black holes (PBHs). First, the non-Gaussian probability is used to compute corrections to the number of PBHs generated from the primordial curvature fluctuations. Particular characteristics of such corrections are explored for a variety of inflationary models. The non-Gaussian corrections explored consist exclusively of non-vanishing three-point correlation functions. 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. The latter has so far been ignored in the estimation of the probability of PBH formation. We account for this by using two parameters to describe the profile: The amplitude of the inhomogeneity and its second radial derivative, both evaluated at the centre of the configuration. The method developed to derive the non-Gaussian PDF is modified to find the joint probability of these two parameters. We discuss the implications of the derived probability for the fraction of mass in the universe in the form of PBHs.