Loop quantum cosmology

Loop quantum cosmology (LQC) is a finite, symmetry-reduced model of loop quantum gravity (LQG) that predicts a "quantum bridge" between contracting and expanding cosmological branches. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of loop quantum gravity (LQG). In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction and thereby resolving singularities of general relativity. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues—e.g., the "horizon problem"—from a new perspective. Since LQG is based on a specific quantum theory of Riemannian geometry, geometric observables display a fundamental discreteness that play a key role in quantum dynamics: While predictions of LQC are very close to those of quantum geometrodynamics (QGD) away from the Planck regime, there is a dramatic difference once densities and curvatures enter the Planck scale. In LQC the Big Bang is replaced by a quantum bounce. Study of LQC has led to many successes, including the emergence of a possible mechanism for cosmic inflation, resolution of gravitational singularities, as well as the development of effective semi-classical Hamiltonians. This subfield originated in 1999 by Martin Bojowald, and further developed in particular by Abhay Ashtekar and Jerzy Lewandowski, as well as Tomasz Pawłowski and Parampreet Singh, et al. In late 2012 LQC represented a very active field in physics, with about three hundred papers on the subject published in the literature. There has also recently been work by Carlo Rovelli, et al. on relating LQC to spin foam cosmology. However, the results obtained in LQC are subject to the usual restriction that a truncated classical theory, then quantized, might not display...