Primordial black holes as a tool for constraining non-Gaussianity

Primordial Black Holes (PBH's) can form in the early Universe from the collapse of large density fluctuations. Tight observational limits on their abundance constrain the amplitude of the primordial fluctuations on very small scales which can not otherwise be constrained, with PBH's only forming from the extremely rare large fluctuations. The number of PBH's formed is therefore sensitive to small changes in the shape of the tail of the fluctuation distribution, which itself depends on the amount of non-Gaussianity present. We study, for the first time, how quadratic and cubic local non-Gaussianity of arbitrary size (parameterised by f_nl and g_nl respectively) affects the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly we find that even non-linearity parameters of order unity have a significant impact on the PBH abundance. The sign of the non-Gaussianity is particularly important, with the constraint on the allowed fluctuation amplitude tightening by an order of magnitude as f_nl changes from just -0.5 to 0.5. We find that if PBH's are observed in the future, then regardless of the amplitude of the fluctuations, non-negligible negative f_nl would be ruled out. Finally we show that g_nl can have an even larger effect on the number of PBH's formed than f_nl.Comment: 9 pages, 5 figures, v2: version to appear in Phys. Rev. D with minor changes, v3: typos corrected (including factor of 1/2 in erfc prefactor), no changes to result

A systems approach to the evaluation of an academic department as a service provider at a University of Technology.

Doctor of Philosophy in Leadership Studies. University of KwaZulu-Natal, Westville 2013.Empirical studies have established that the services sector has contributed significantly to the growth and development of world economies and is today the largest and fastest growing sector globally. Testimony to the rise in the supply of services is the fact that the services sector contributes more to the global output and employs more people than any other sector. It has been widely accepted that education belongs to the category of service industries, resulting in the importance of rendering a quality service. In South Africa, although education is the recipient of the major portion of national expenditure, government funding to tertiary institutions has been on the decline, prompting institutions of higher learning to develop innovative methods to maintain financial stability. One of the strategies has been to attract and retain national and international students by the rendering of a quality service. The purpose of this research is to provide a conceptual framework for gaining a better understanding of evaluation of an academic department as a service provider at a university of technology. The task is viewed as complex as a university is regarded as a highly bureaucratic organisation intertwined with other systems, subsystems and various stakeholders. An investigation into the current state of practice and research into evaluation of academic departments is reported. A review of the research issues on service organisations and their applicability to tertiary institutions is presented. The framework was developed upon principles of Multimethodology, using a combination of the strengths of Critical Systems Thinking, Soft Systems Methodology, Viable System Method, System Dynamics, Work System Method and the Analytic Hierarchy Process by Saaty. This framework is applied to a case study at an academic department of the Durban University of Technology