​Super-Renormalizable Quantum Gravity

The greatest physicists of the 20th century were able to find a consistent (renormalizable) quantum field theory for all fundamental interactions except for gravity. Starting from quantum electrodynamics and quantum non-abelian gauge theories up to the standard model of particle physics to the recent discovery of the Higgs boson, two guiding principles seem to dominate the research in high-energy physics: "renormalization and perturbative theory". However, gravity seems to elude so far these patterns and many authors suggest ingenious solutions to one of the biggest puzzles of our days, but none is completely satisfactory. But first and foremost, how we can be sure about the quantum nature of gravity at very short distance? There are  many reasons to believe that gravity has to be quantum, some of which are: the quantum nature of matter in the right-hand side of the Einstein equations, the singularities appearing in classical solutions of general relativity, the discovery of the gravitational waves, etc. However, the major obstacle when we try to construct a consistent theory of quantum gravity is that Einstein dynamics is "non-renormalizable" by conventional quantum field criteria and hence it is not capable to tame in any way the ambiguous predictions coming out at quantum level.

It is common belief that general relativity and quantum mechanics are not compatible, but there is nothing inconsistent between them. Just like the Fermi theory of weak interactions, quantum Einstein gravity is solid and calculable as well as Fermi theory makes predictions for weak interactions. Einstein's gravity is just non-renormalizable, and at high energy E =Mp (Planck mass) higher order operators in the Lagrangian become decisive. Therefore, if we want to use a diffeomorphism invariant action for a massless spin two particle at short distances, we need an ultraviolet completion of Einstein gravity. In the last six years our main goal has been to extend the classical Einstein-Hilbert theory to make gravity compatible with the above guiding principles (renormalization and perturbative theory)  in the "quantum field theory framework". And finally we recently managed to find a completion of Einstein classical gravity compatible with the following minimal requirements.

1. Unitarity. A general theory is well defined if "tachyons" and "ghosts" are absent, in which case the
corresponding propagator has only first poles with real masses (no tachyons) and with positive residues (no ghosts).

2.  Super-renormalizability or finiteness. This hypothesis makes consistent the theory at quantum level in analogy with all the other fundamental interactions.

3. Lorentz invariance. This is a symmetry of nature well tested experimentally below the Planck scale.