Composite graviton self-interactions in a model of emergent gravity

TL;DR

This paper investigates the self-interactions of a composite graviton in a covariant scalar field model, showing that these interactions align with Einstein's gravity and are universal across different scalar types.

Contribution

It demonstrates that the emergent graviton's cubic self-interactions match Einstein gravity and are universal, under conditions ensuring a massless spin-2 state and a vanishing cosmological constant.

Findings

Emergent graviton self-interactions are consistent with Einstein's gravity.

The graviton coupling is universal across multiple scalar types.

Fine-tuning conditions support the emergence of a massless spin-2 state.

Abstract

We consider a theory of scalars minimally coupled to an auxiliary background metric. The theory is generally covariant and subject to the constraint of vanishing energy-momentum tensor. Eliminating the auxiliary metric leads to a reparametrization invariant, non-polynomial, metric-independent action for the scalar fields. Working in the limit of a large number of physical scalars, a composite massless spin-2 state, the graviton, was identified in previous work, in a two-into-two scalar scattering process. Here, we further explore the possibility that dynamical emergent gravity is a natural feature of generally covariant quantum field theories, by studying the self-interactions of the emergent composite graviton. We show that the fine-tuning previously imposed to ensure the vanishing of the cosmological constant, as well as the existence of the massless spin-2 state, also assures that the emergent graviton's cubic self-interactions are consistent with those of Einstein's general relativity, up to higher-derivative corrections. We also demonstrate in a theory with more than one type of scalar that the composite graviton coupling is universal.