Reviews developments in applications of inhomogeneous models to cosmology, for graduate students and academic researchers in astrophysics.

Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau functions.

This book mathematically derives the theory underlying the Belinski-Khalatnikov-Lifshitz conjecture on the general solution of the Einstein equations with a cosmological singularity.

A comprehensive account of new models of extra dimensions which form an important part of present-day high-energy physics.

An elementary introduction to hadronic properties at finite temperature and density that develops real-time methods of thermal field theory.

The past two decades have seen transformative advances in cosmology and string theory. Observations of the cosmic microwave background have revealed strong evidence for inflationary expansion in the very early universe, while new insights about compactifications of string theory have led to a deeper understanding of inflation in a framework that unifies quantum mechanics and general relativity. Written by two of the leading researchers in the field, this complete and accessible volume provides a modern treatment of inflationary cosmology and its connections to string theory and elementary particle theory. After an up-to-date experimental summary, the authors present the foundations of effective field theory, string theory, and string compactifications, setting the stage for a detailed examination of models of inflation in string theory. Three appendices contain background material in geometry and cosmological perturbation theory, making this a self-contained resource for graduate students and researchers in string theory, cosmology, and related fields.

The year 2011 marked the 80th anniversary of Georges Lemaître’s primeval atom model of the universe, forerunner of the modern day Big Bang theory. Prompted by this momentous anniversary the Royal Astronomical Society decided to publish a volume of essays on the life, work and faith of this great cosmologist, who was also a Roman Catholic priest. The papers presented in this book examine in detail the historical, cosmological, philosophical and theological issues surrounding the development of the Big Bang theory from its beginnings in the pioneering work of Lemaître through to the modern day. This book offers the best account in English of Lemaître’s life and work. It will be appreciated by professionals and graduate students interested in the history of cosmology.