From Linear Gravity Up

The linearized theory of gravity - the lowest-order terms in the Einstein Field Equation (EFE) - describes a force exchanged by a massless, spin-2 field, representing the perturbation of the metric relative to a flat background. The remaining, nonlinear terms of the EFE may then be thought of as self-interactions of that field. In this talk, I will present two advances that shed light on different aspects of gravitational theory, as seen from this “perturbative General Relativity” point of view.

I will first present a new way of deriving the EFE itself, taking the linear part as a starting point. As Feynman made famous, the self-interaction terms are expected even from purely field-theoretic reasoning, as follows. For consistency, gravity must couple to all forms of energy, including that of the gravitational field itself. So a gravitational energy term, quadratic in the field, must appear together with the other sources in the EFE. But the presence of this term then implies a cubic contribution to the field energy, and so on order by order, until we “bootstrap” to the full EFE. However, the idea of “the energy of the field itself” is not specific enough, on its own, to determine the exact terms. The derivations until now have proceeded in ways heavily inspired by our knowledge of Einstein’s theory and its symmetries, weakening the claim of a derivation from pure field theory. We show for the first time that no such knowledge is needed. We can get all of the self-interactions using only the requirement that our field equation should come from some Lagrangian. 

In the second part of the talk, I will discuss the quantum version of the theory. Perturbative GR can be straightforwardly quantized as a Low-Energy Effective Field Theory, with the spin-2 field interpreted as a “graviton”. We can then calculate quantum corrections to the classical theory of General Relativity. We have upgraded a program automating effective field theory calculations, called MatchMakerEFT, to enable working with spin-2 fields. Using this tool, we automatically compute some of these quantum corrections. We have also computed such corrections for an alternative theory called dRGT Massive Gravity, for which such corrections were not yet known.