Toward a Mechanism for the Emergence of Gravity

Abstract

One of the main problems that emergent-gravity approaches face is explaining how a system that does not contain gauge symmetries ab initio might develop them effectively in some regime. We review a mechanism introduced by some of the authors for the emergence of gauge symmetries in [JHEP 10 (2016) 084] and discuss how it works for interacting Lorentz-invariant vector field theories as a warm-up exercise for the more convoluted problem of gravity. Then, we apply this mechanism to the emergence of linear diffeomorphisms for the most general Lorentz-invariant linear theory of a two-index symmetric tensor field, which constitutes a generalization of the Fierz–Pauli theory describing linearized gravity. Finally we discuss two results, the well-known Weinberg–Witten theorem and a more recent theorem by Marolf, that are often invoked as no-go theorems for emergent gravity. Our analysis illustrates that, although these results pinpoint some of the particularities of gravity with respect to other gauge theories, they do not constitute an impediment for the emergent gravity program if gauge symmetries (diffeomorphisms) are emergent in the sense discussed in this paper.

Unimodular gravity vs general relativity: a status report

“…This is the source of the potential non-uniqueness of the procedure and, to the authors' knowledge, a proof of the uniqueness of GR is still missing. Further details of the bootstrapping procedure can be found in [39][40][41].…”

Bootstrapping gravity and its extension to metric-affine theories

“…Such a tensor can be consistently defined in the context of the geometrical trinity [22,26] which is outside the scope of this article, but otherwise it is known that there is no local definition of energy-momentum tensor for the gravitational field in a diffeomorphism-invariant theory. Therefore, either we construct a non-gauge-invariant tensor (which would be hard to be given a clear physical meaning), or we construct a non-conserved quantity [27][28][29]. We will refer to the gravitational energy-momentum as the conserved tensor computed following the procedures outlined in the section above, and we will analyze the gauge invariance of the full non-linear action once the bootstrapping is finished.…”

“…In addition to understand some questions raised in previous works on the topic, our results are interesting also for several reasons. Regarding embedding metric-affine theories of gravity into emergent approaches, the bootstrapping procedure is a key tool [29,35,36]. Although in emergent approaches it is easy to analyze the degrees of freedom that can arise in linearized theories around a Fermi-point, it is hard to understand the potential non-linear completions of such theories without further insights.…”

Analogue gravity simulation of superpositions of spacetimes

“…The philosophy underlying the analogue gravity program and in a more complete sense, emergent gravity scenarios (i.e. hypothetical scenarios in which Einstein equations are also emergent [64]) is that everything that we perceive is constituted by low-energy collective excitations of some fundamental microscopic degrees of freedom. For instance, the spacetime itself and the quantum fields describing the Standard Model of Particle Physics would be part of such collective excitations.…”