The quantization of gravity and the vacuum energy of quantum fields

TL;DR

This paper proposes a unified covariant framework combining gravity and gauge fields, showing that vacuum energy cancels out at low energies and that gravity's weakness is linked to quantum vacuum energy.

Contribution

It introduces a covariant derivative unifying affine connection and Yang-Mills fields, and demonstrates a mechanism for vacuum energy cancellation and emergent General Relativity.

Findings

Vacuum energy cancels at low energies, recovering General Relativity.

The theory suggests gravity is weak due to large quantum vacuum energy.

At high energies, the metric acts as a classical background, with connections as quantum fields.

Abstract

We construct a unified covariant derivative that contains the sum of an affine connection and a Yang-Mills field. With it we construct a lagrangian that is invariant both under diffeomorphisms and Yang-Mills gauge transformations. We assume that metric and symmetric affine connection are independent quantities, and make the observation that the metric must be able to generate curvature, just as the connection, so there should be an extra tensor similar to Riemann's in the equations but constructed from metrics and not connections. We find the equations generated by the lagrangian and introduce the huge natural scale due to the vacuum energy of quantum fields. This scale allows for a perturbative solution of the equations of motion. We prove the system has a vacuum state that forces the metricity of the metric and results in General Relativity for low energies. The vacuum energy of the quantum fields cancels, becoming unobservable. At very high energies, the metric does not appear differentiated in the lagrangian and so it is not a quantum field, just a background classical field. The true quantum fields are the connections. The theory becomes very similar to a Yang-Mills, with affine connections taking the place of Yang-Mills vector fields. It should be renormalizable since it has a coupling constant with no units and correct propagators after fixing the gauge (diffeomorphisms). The weakness of gravity turns out to be due to the large vacuum energy of the quantum fields.