Constraints on emergent gravity

Abstract

In this essay we review the central difficulty in formulating a viable quantum field theory in which gravity is emergent at low energies, rather than mediated by a fundamental gauge field. The Weinberg-Witten theorem forbids spin 2 massless modes from carrying Lorentz covariant stress-energy. In General Relativity the stress-energy is not covariant because it violates a gauge symmetry, but a gravitational theory without fundamental spin 2 gauge invariance must either lack a stress-energy operator or have a non-relativistic graviton. The latter option is incompatible with the principle of equivalence, though such theories are not necessarily ruled out at low energies.

8 pages, 1 figure, preprint format. Submitted to the Gravity Research Foundation 2009 Awards for Essays on Gravitation. Awarded honorable mention, to appear in special issue of IJMPD. v2: references improved, minor points clarified