Cosmology

This book is aimed at theoretical and mathematical physicists and mathematicians interested in modern gravitational physics. I have thus tried to use language familiar to readers working on classical and quantum gravity, paying attention both to difficult calculations and to existence theorems, and discussing in detail the current literature. The first aim of the book is to describe recent work on the problem of boundary conditions in one-loop quantum cosmology. The motivation of this research was to under­ stand whether supersymmetric theories are one-loop finite in the presence of boundaries, with application to the boundary-value problemsoccurring in quantum cosmology. Indeed, higher-loop calculations in the absence of boundaries are already available in the litera­ ture, showing that supergravity is not finite. I believe, however, that one-loop calculations in the presence of boundaries are more fundamental, in that they provide a more direct check of the inconsistency of supersymmetric quantum cosmology from the perturbative point of view. It therefore appears that higher-order calculations are not strictly needed, if the one-loop test already yields negative results. Even though the question is not yet settled, this research has led to many interesting, new applications of areas of theoretical and mathematical physics such as twistor theory in flat space, self-adjointness theory, the generalized Riemann zeta-function, and the theory of boundary counterterms in super­ gravity. I have also compared in detail my work with results by other authors, explaining, whenever possible, the origin of different results, the limits of my work and the unsolved problems.

This book provides a comprehensive account of Kant’s development from the 1755/56 metaphysics to the cosmological antinomy of 1781. With the Theory of the Heavens (1755) and the Physical Monadology (1756), the young Kant had presented an ambitious approach to physical cosmology based on an atomistic theory of matter, which contributed to the foundations of an all-encompassing system of metaphysics.

With the aid of entertaining short stories, anecdotes, lucid explanations and straight-forward figures, this book challenges the perception that the world of physics is inaccessible to the non-expert. Beginning with Neanderthal man, it traces the evolution of human reason and understanding from paradoxes and optical illusions to gravitational waves, black holes and dark energy. On the way, it provides insights into the mind-boggling advances at the frontiers of physics and cosmology.