Abstract
The Planck scale (10-35m) is a fundamental limit for quantum gravity. At this scale, the idea of smooth space collapses. If we want to have enough energy to localize a particle, this energy is such that it creates its own black hole. Black holes play a major role in quantum gravity. Black holes evaporate thanks to the existence of the quantum vacuum and its virtual particles. String theory can give a representation of quantum gravity, and justify the microscopic origin of Bekenstein-Hawking entropy. Part of the solution to the problem of lost entropy in black holes can be found in the holographic principle: the information contained in the volume bounded by the black hole's horizon cannot be greater than that contained on its surface. There is a quantum of entropy (or information) that is a quarter of the Planck surface. The black hole's entropy is therefore less than a quarter of its surface.
Models of modified gravity range from theories in which the Ricci R is replaced by f(R), to theories in which one or more scalar, or even vector, fields are added, such as the tensor-scalar-vector theory TeVeS, which reproduces the ideas and successes of MOND for observations of galaxies, without dark matter. There are also a large number of extra-dimensional models, where only gravity propagates in other dimensions. It is possible to generalize to generic Horndeski tensor-scalar models, presented by Cédric Deffayet. Since 2010, it has also been possible to imagine that the graviton has mass, as the ghost that prevented the production of a nonlinear theory of massive gravity has been resolved. To study string theory, it is convenient to use anti-de Sitter (AdS) spaces with negative cosmological constant, and the AdS/CFT (conformal field theory) equivalence principle. Gravity can then be equivalent to a field theory. The combination of the holographic principle and the correspondence between temperature and acceleration (for black holes, cf. Unruh) led to Erik Verlinde's hypothesis that gravitation is not a fundamental force but an entropic force. Variations in quantum entanglement entropy, due to the presence of matter, could explain the emergence of gravity. Another possibility is quantum loop theory, which creates its own space-time.
