Primordial black holes in non-linear perturbation theory

The thesis begins with a study of the origin of non-linear cos m logical fluctuations. In particular, a class of models of multiple field inflation are conside red, with specific reference to those cases in which the non-Gaussian correlation functions are l arge. The analysis shows that perturbations from an almost massless auxiliary field generically produce large values of the non-linear parameterfNL. Next, the effects of including non-Gaussian correlation fu ctions in the statistics of cosmological structure are explored. For this purpose, a non-Gau ssi n probability distribution function (PDF) for the curvature perturbation R is required. Such a PDF is derived from first principles in the context of quantum field theory, with n-point correlatio n functions as the only input. Under reasonable power-spectrum conditions, an explicit expres sion for the PDF is presented, with corrections to the Gaussian distribution from the three-point correlation function〈RRR〉. 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 ho les (PBHs). First, the non-Gaussian probability is used to compute corrections to the number of P BHs generated from the primordial curvature fluctuations. Particular characteristics of suc h corrections are explored for a variety of inflationary models. The non-Gaussian corrections explore d consist exclusively of non-vanishing three-point correlation functions. The second application concerns new cosmological observab l s. The formation of PBHs is known to depend on two main physical characteristics: the st reng h of the gravitational field produced by the initial curvature inhomogeneity and the pre ssure gradient at the edge of the curvature configuration. The latter has so far been ignored i n the estimation of the probability of PBH formation. We account for this by using two parameters o describe the profile: The amplitude of the inhomogeneity and its second radial deriva tive, both evaluated at the centre of the configuration. The method developed to derive the non-Ga ussi n PDF is modified to find the joint probability of these two parameters. We discuss the im plications of the derived probability for the fraction of mass in the universe in the form of PBHs. I hereby certify that this thesis, which is approximately 45, 000 words in length, has been written by me, that it is the record of the work carried out by m e at the Astronomy Unit, Queen Mary, University of London, and that it has not been sub mitted in any previous application for a higher degree. Some of the work contained in Chapter 2 was carried out in coll ab ration with Dr David Seery and Dr Filippo Vernizzi and is unpublished. Chapter 3 p esents a project developed in collaboration with Dr David Seery, published as an articl e in the Journal of Cosmology and Astroparticle Physics [Seery & Hidalgo, 2006]. The work in Chapter 4 was done by me alone and it is described in an article available on-line [ Hidalgo, 2007]. The material in Chapter 5 was done in collaboration with Dr Alexander Polnar ev and is published in Physical Review D [Hidalgo & Polnarev, 2009]. I made a major contr ibution to all the original research presented in this thesis. Juan Carlos Hidalgo Queen Mary, University of London London, United Kingdom April, 2009