An overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.

The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.

This book summarizes recent developments in the research area of quantum gravity phenomenology. A series of short and nontechnical essays lays out the prospects of various experimental possibilities and their current status. Finding observational evidence for the quantization of space-time was long thought impossible. In the last decade however, new experimental design and technological advances have changed the research landscape and opened new perspectives on quantum gravity. Formerly dominated by purely theoretical constructions, quantum gravity now has a lively phenomenology to offer. From high precision measurements using macroscopic quantum oscillators to new analysis methods of the cosmic microwave background, no stone is being left unturned in the experimental search for quantum gravity. This book sheds new light on the connection of astroparticle physics with the quantum gravity problem. Gravitational waves and their detection are covered. It illustrates findings from the interconnection between general relativity, black holes and Planck stars. Finally, the return on investment in quantum-gravitation research is illuminated. The book is intended for graduate students and researchers entering the field.

In this XVII Course of the International School of Cosmology and Gravitation devoted to "ADVANCES IN THE INTERPLAY BETWEEN QUANTUM AND GRAVITY PHYSICS" we have considered different aspects of the influence of gravity on quantum systems. In order to achieve this aim, in many lectures, seminars and discussions we have strengthened the interplay between gravity and quantum systems starting from the situation in the early universe based on astrophysical observations, up to the earthly based experiments with atom interferometry for probing the structure of space-time. Thus we have had timely lectures on the quantum field and horizon of a black hole including reviews of the problem of black holes thermodynamics and entropy, quantum information, quantum black holes, quantum evaporation and Hawking radiation, recent advances in stockastic gravity. We have also discussed quantum fluctuations in inflationary universe, quantum effects and reheating after inflation, and superplanckian energies in Hawking radiation. In this regard the subject of spinors in purely affine space-time and Dirac matter according to Weyl in the generalized theory of gravitation were developed . The dualism between space-time and matter has been deeply analyzed in order to see why, for general relativity, this is an obstacle for quantization of the theory. Also canonical Gravity and Mach's principle, torsion and curvature as commutator for Quantum Gravity and Dirac Geometry of real space-time were analysed, together with the problem of 5-Dimensional Projective Unified Field theory and Multidimensional Gravity and Cosmology.

"Quantum Gravitation" approaches the subject from the point of view of Feynman path integrals, which provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. It is shown that the path integral method is suitable for both perturbative as well as non-perturbative studies, and is already known to offer a framework for the theoretical investigation of non-Abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. The final chapter addresses contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.