Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom

TL;DR

This paper constructs an infinite class of effective metric Lagrangians with two propagating degrees of freedom, showing they can be related to Einstein-Hilbert gravity via non-local field redefinitions, and are consistent with quantum gravity divergences.

Contribution

It introduces a new class of effective metric Lagrangians with two degrees of freedom, linked to quantum gravity divergences, and demonstrates their equivalence to Einstein-Hilbert gravity through non-local transformations.

Findings

Effective Lagrangians include R^2, (Ricci)^2, and (Riemann)^3 terms.

A non-local field redefinition maps these Lagrangians to Einstein-Hilbert form.

The structure explains why such theories have only two propagating degrees of freedom.

Abstract

We describe an infinite-parametric class of effective metric Lagrangians that arise from an underlying theory with two propagating degrees of freedom. The Lagrangians start with the Einstein-Hilbert term, continue with the standard R^2, (Ricci)^2 terms, and in the next order contain (Riemann)^3 as well as on-shell vanishing terms. This is exactly the structure of the effective metric Lagrangian that renormalizes quantum gravity divergences at two-loops. This shows that the theory underlying the effective field theory of gravity may have no more degrees of freedom than is already contained in general relativity. We show that the reason why an effective metric theory may describe just two propagating degrees of freedom is that there exists a (non-local) field redefinition that maps an infinitely complicated effective metric Lagrangian to the usual Einstein-Hilbert one. We describe this map for our class of theories and, in particular, exhibit it explicitly for the (Riemann)^3 term.