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 2001 book explains the construction of exact soliton solutions to Einstein's theory of gravity.

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.

The characteristic – Planck – energy scale of quantum gravity makes experimental access to the relevant physics apparently impossible. Nevertheless, low energy experiments linking gravity and the quantum have been undertaken: the Page and Geilker quantum Cavendish experiment, and the Colella-Overhauser-Werner neutron interferometry experiment, for instance. However, neither probes states in which gravity remains in a coherent quantum superposition, unlike – it is claimed – recent proposals. In essence, if two initially unentangled subsystems interacting solely via gravity become entangled, then theorems of quantum mechanics show that gravity cannot be a classical subsystem. There are formidable challenges to such an experiment, but remarkably, tabletop technology into the gravity of very small bodies has advanced to the point that such an experiment might be feasible in the near future. This Element explains the proposal and what it aims to show, highlighting the important ways in which its interpretation is theory-laden.