Composite graviton self-interactions in a model of emergent gravity

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, nonpolynomial, 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.

Composite gravitons from metric-independent quantum field theories

“…In this section, we review the approach of Refs. [4,5] towards analyzing the theory defined in Eq. (1.1).…”

“…In particular, it was argued in Refs. [4,5] that the two-into-two scattering of scalars of type a into type c, with a = c, and at leading order in 1/N , gives the set of scattering diagrams shown in where the factors of E µν represent the Feynman rule for the flat-space energy-momentum tensor in Eq. (2.4),…”

“…(2.12) displays the correct tensor structure for the gaugeinvariant part of the propagator of a massless, spin-two field. A similar diagrammatic study of two-into-four scattering in the same theory was employed to study the self-interactions of the composite graviton state and the results were found to be consistent with Einstein gravity, up to higher-derivative corrections [5]. We do not summarize that more burdensome calculation here, but refer the reader to the original literature.…”

“…The present mini-review describes quantum field theory models of this type, proposed by Carone, Erlich and Vaman [4,5], that are designed to produce an emergent graviton in the infrared 1 . We will focus primarily on a model of scalar fields in this review, since all the relevant features of this framework can be illustrated with the fewest technical complications.…”

“…Refs. [4,5] is interpreted consistently as the massless limit of a massive composite gravity model, where the graviton mass does not have the Pauli-Fierz form. Since this implies the presence of ghosts, we discuss how that can be avoided by an alternative formulation in Sec.…”