Symmetries from Locality. III. Massless Spin 2 Gravitons and Time Translations

TL;DR

This paper explores the conditions under which massless spin 2 gravitons can exist without assuming time translation or Lorentz boost symmetry, showing that locality constrains their organization into Einstein-Hilbert plus Gauss-Bonnet terms with specific time dependence.

Contribution

It demonstrates that locality of the exchange action constrains the form of massless spin 2 gravitons to Einstein-Hilbert plus Gauss-Bonnet terms, even without assuming time translation or Lorentz boost symmetry.

Findings

Locality constrains graviton organization to Einstein-Hilbert plus Gauss-Bonnet terms.

Time dependence of the Gauss-Bonnet prefactor is constrained at leading order.

Matter sector recovers time translation and Lorentz boost symmetry.

Abstract

We relax the assumption of time translation and Lorentz boost symmetry in theories involving massless spin 2 gravitons, while maintaining a basic notion of locality that there is no instantaneous signaling at a distance. We project out longitudinal modes, leaving only two degrees of freedom of the graviton. Our previous work, which assumed time translation symmetry, found that the Lorentz boost symmetry is required to ensure locality at leading order. In this work, without assuming time translations or Lorentz boosts, we show that locality of the exchange action between matter sources demands that massless spin 2, at leading order, organizes into Einstein-Hilbert plus a Gauss-Bonnet term with a prefactor that is constrained to be a particular function of time; while in the matter sector we recover time translation and Lorentz boost symmetry. Finally, we comment on whether the time dependence of the Gauss-Bonnet prefactor may be forbidden by going to higher order in the analysis and we mention that other possibilities are anticipated if graviton mass terms are included.