Elementary Cosmology

Just before the preliminary program of Orbis Scientiae 1998 went to press the news in physics was suddenly dominated by the discovery that neutrinos are, after all, massive particles. This was predicted by some physicists including Dr. Behram Kusunoglu, who had apaper published on this subject in 1976 in the Physical Review. Massive neutrinos do not necessarily simplify the physics of elementary particles but they do give elementary particle physics a new direction. If the dark matter content of the universe turns out to consist of neutrinos, the fact that they are massive should make an impact on cosmology.

In this book, the author leads the reader, step by step and without any advanced mathematics, to a clear understanding of the foundations of modern elementary particle physics and cosmology. He also addresses current and controversial questions on topics such as string theory. The book contains gentle introductions to the theories of special and general relativity, and also classical and quantum field theory. The essential aspects of these concepts are understood with the help of simple calculations; for example, the force of gravity as a consequence of the curvature of the space-time.

This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition.

This thesis explores the idea that the Higgs boson of the Standard Model and the cosmological inflation are just two manifestations of one and the same scalar field - the Higgs-inflation. By this unification two energy scales that are separated by many orders of magnitude are connected, thereby building a bridge between particle physics and cosmology. An essential ingredient for making this model consistent with observational data is a strong non-minimal coupling to gravity. Predictions for the value of the Higgs mass as well as for cosmological parameters are derived, and can be tested by future experiments. The results become especially exciting in the light of the recently announced discovery of the Higgs boson.

This volume is based on the lectures given at the First Inter University Graduate School on Gravitation and Cosmology organized by IUCAA, Pune, in 1989. This series of Schools have been carefully planned to provide a sound background and preparation for students embarking on research in these and related topics. Consequently, the contents of these lectures have been meticulously selected and arranged. The topics in the present volume offer a firm mathematical foundation for a number of subjects to be de­ veloped later. These include Geometrical Methods for Physics, Quantum Field Theory Methods and Relativistic Cosmology.