Session X12: Recent Developments in Quantum Gravity

Recent Advances in Loop Quantum Cosmology

Einstein's theory of classical general relativity explains the dynamics of our universe at low energies to an excellent precision. However, it breaks down at the Planck scale before the big bang singularity is reached. Relativity thus fails to tell us about the origin of our cosmos and leaves open various questions which are expected to be answered by a quantum theory of gravity. We will review recent developments in loop quantum cosmology which is a quantization of cosmological spacetimes based on loop quantum gravity -- a non-perturbative background independent quantization of gravity. Because, of fundamental discreteness of quantum geometry underlying loop quantum gravity, novel features arise. In particular, for quantum states representing a large classical universe at late times there is an upper bound on the gravitational curvature, of the order of $1/(\mathrm{Planck ~~ length})^2$. Thus, non-perturbative quantum gravity effects forbid the cosmological dynamics from entering a regime where curvature or energy density blow up. Evolution in loop quantum cosmology is non-singular. In models studied so far, the backward evolution of our expanding universe does not lead to a big bang but a big bounce to a contracting branch when the gravitational curvature reaches Planck scale. These results which have now been established for various homogeneous spacetimes provide a new paradigm of the genesis of our universe and lead to useful insights on the generic resolution of space-like singularities through quantum gravity effects.   

Graviton propagator from Loop Quantum Gravity

Loop quantum gravity provides a background independent quantisation of General Relativity, where the microscopical structure of spacetime shows discrete and quantum properties. This microscopical quantum geometry has led to new insights in problems such as the big bang and black hole singularities. However, the study of the semiclassical limit of the theory is still a key open issue. In this talk, I will present recent developments suggesting that the correct low energy physics emerges. In particular, I will describe how the calculations of the graviton propagator in loop quantum gravity agree at large scales with the conventional free propagator of linearised General Relativity, and how the microscopical quantum geometry is likely to provide new and non--trivial quantum corrections to it.   

The Asymptotic Safety Scenario in Quantum Gravity

The Asymptotic Safety Scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. All presently known evidence is surveyed: (a) from the $2+\backslash eps$ expansion, (b) from renormalizable higher derivative gravity theories and a `large $N$' expansion in the number of matter fields, (c) from symmetry reductions modeling the residual selfinteractions in the ultraviolet, and (d) from truncated flow equations for the effective average action. Special emphasis is given to the role of perturbation theory as a guide to `asymptotic safety'. Further it is argued that as a consequence of the scenario the selfinteractions appear two-dimensional in the extreme ultraviolet.