The present book is based on the author’s Ph.D. thesis, accepted by the University of Cologne, Germany in 2012. The book is based on five published articles. The main subject of the book combines general relativity, more specifically, cosmology, with quantum field theory and elementary particle physics. The idea is to consider the Higgs field as the scalar field responsible for the initial inflationary expansion of the Universe. An additional complication to this idea is that it will only work if one introduces a strong non-minimal coupling between the Higgs field and the gravitational field.
In the initial chapters of the book, the author gives an introduction to the most important aspects of cosmology, quantum field theory and elementary particle physics needed to the description of the non-minimal Higgs inflation model. Chapter five is dedicated to the calculation of the one-loop effective action for an \(\mathrm{O}(N)\)-symmetric multiplet of scalar fields non-minimally coupled to gravity. Also, in this chapter, the author demonstrates that the quantum field theory description, of the above model, in the “Jordan frame” and in the “Einstein frame” are not equivalent. The most important chapter of the book is the sixth. There, the author derives the physical predictions from the non-minimal Higgs inflation model. In chapter seven, the author computes the tunneling wave-function of the Universe, for the non-minimal Higgs inflation model, using the path integral formalism of quantum cosmology. After, obtaining the appropriate partition function the author is able to predict initial conditions for the inflationary expansion of the Universe. Chapter eight is dedicated to the conclusions and the book ends with seven appendices.